This note is to investigate the properties of strongly semipotent rings.It is proved that every strongly semipotent ring is a idempotent unit regular ring,i.e.,there exist a non-zero idempotent e and a unit u such tha...This note is to investigate the properties of strongly semipotent rings.It is proved that every strongly semipotent ring is a idempotent unit regular ring,i.e.,there exist a non-zero idempotent e and a unit u such that er=eu for all r∉J(R),where J(R)is the Jacobson radical of ring R.展开更多
The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- reg...The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.展开更多
An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of...An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.展开更多
Let R be a ring and J（R） the Jacobson radical. An element a of R is called（strongly） J-clean if there is an idempotent e ∈ R and w ∈ J（R） such that a = e ＋ w（and ew = we）. The ring R is called a（strongly）...Let R be a ring and J（R） the Jacobson radical. An element a of R is called（strongly） J-clean if there is an idempotent e ∈ R and w ∈ J（R） such that a = e ＋ w（and ew = we）. The ring R is called a（strongly） J-clean ring provided that every one of its elements is（strongly） J-clean. We discuss, in the present paper,some properties of J-clean rings and strongly J-clean rings. Moreover, we investigate J-cleanness and strongly J-cleanness of generalized matrix rings. Some known results are also extended.展开更多
For a monoid M, we introduce the concept of skew strongly M-reversible rings which is a generalization of strongly M-reversible rings, and investigate their properties. It is shown that if G is a finitely generated Ab...For a monoid M, we introduce the concept of skew strongly M-reversible rings which is a generalization of strongly M-reversible rings, and investigate their properties. It is shown that if G is a finitely generated Abelian group, then G is torsion-free if and only if there exists a ring R with 丨R丨 ≥ 2 such that R is skew strongly G-reversible. Moreover, we prove that if R is a right Ore ring with classical right quotient ring Q, then R is skew strongly M-reversible if and only if Q is skew strongly M-reversible.展开更多
?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent sem...?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.展开更多
For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring ...For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring Q, we prove that R is strongly M-α-reflexive if and only if Q is strongly M-α-reflexive, where R is α-rigid, α is an epimorphism of R. The relationship between some special subrings of upper triangular matrix rings and strongly M-α-reflexive rings is also investigated. Several known results similar to strongly M-α-reversible rings are obtained.展开更多
We in this note introduce a new concept,so called strongly J-semiclean ring,that is a generalization of strongly J-clean rings.We first observe the basic properties of strongly J-semiclean rings,constructing typical e...We in this note introduce a new concept,so called strongly J-semiclean ring,that is a generalization of strongly J-clean rings.We first observe the basic properties of strongly J-semiclean rings,constructing typical examples.We next investigate conditions on a local ring R that imply that the upper triangular matrix ring Tn(R)is a strongly J-semiclean ring.Also,the criteria on strong J-semicleanness of 2×2 matrices in terms of a quadratic equation are given.As a consequence,several known results relating to strongly J-clean rings are extended to a more general setting.展开更多
In this paper,potent index of an element and pseudo clean rings are considered.Some properties and examples of pseudo clean rings are given.We also show that Zm is pseudo clean for every 2≤m∈Z and pseudo clean rings...In this paper,potent index of an element and pseudo clean rings are considered.Some properties and examples of pseudo clean rings are given.We also show that Zm is pseudo clean for every 2≤m∈Z and pseudo clean rings are clean.Furthermore,we prove pseudo clean rings are directly finite and have stable range one.展开更多
New kinds of strongly zero-dimensional locales are introduced and characterized, which are different from Johnstone's, and almost all the topological properties for strongly zero-dimensional spaces have the pointl...New kinds of strongly zero-dimensional locales are introduced and characterized, which are different from Johnstone's, and almost all the topological properties for strongly zero-dimensional spaces have the pointloss localic forms. Particularly. the Stone-Cech compactification of a strongly zero-diluensional locale is stongly zero-dimensional.展开更多
A systematic study on ″ring phenomena″ frequently occurring before great earthquakes has made in this paper, which has analyzed the features of ring distributions before 16 great earthquakes and part of large ear...A systematic study on ″ring phenomena″ frequently occurring before great earthquakes has made in this paper, which has analyzed the features of ring distributions before 16 great earthquakes and part of large earthquakes in China and its boundary areas, and discussed their features of generality, regularity and predictive meaning. The results have showed that moderate earthquakes or larger earthquakes distribute around the epicenter like a ring from decades to hundred years before the great earthquakes of magnitude more than 7, which is a general phenomenon of great earthquakes without an exception. The active ring generally occurs in the areas from hundreds to thousands of kilometers from the epicenter(according to the magnitude). The seismicity in the ring has three basic stages with different features. in the first stage, seismicity remains at low level and the earthquakes distribute scatteredly, while the source area of the future great earthquake remains quiet; in the second stage, the seismicity strengthens, whose frequency, intensity, concentrated degree, released rate of strain and ratio of distributed area etc. increase, while the quiet area decreases or disappears; in the third stage, the seismicity is weaker than in the former stage, and the quiet area appears again. The source area surrounded by the active ring might have three periods of activity(called as early term, medium term and late term foreshocks activity). The length of the quiet area undergoes the process from large to small, then to large. Therefore, we can estimate the occurring place, magnitude and seismogenic stage of great earthquake according to the area,length and the seismicity in the active ring, which is valuable to make a long term prediction of great earthquakes. At last, we had a preliminary discussion on the mechanism of active ring formation.展开更多
A ring R is called left morphic, if for any a ∈ R, there exists b ∈ R such that lR（a） =Rb and lR（b）= Ra. In this paper, we use the method which is different from that of Lee and Zhou to investigate when R[x, σ]...A ring R is called left morphic, if for any a ∈ R, there exists b ∈ R such that lR（a） =Rb and lR（b）= Ra. In this paper, we use the method which is different from that of Lee and Zhou to investigate when R[x, σ]/（x^n） is （left） morphic and when the ideal extension E（R, V） is （left） morphic. It is mainly shown that： （1） If is an automorphism of a division ring R, then S = R[x, σ]/（x^n） （n 〉 1） is a special ring. （2） If d,m are positive integers and n = dm, then E（Zn, mZn） is a morphic ring if and only if gcd（d, m） = 1.展开更多
Block chain is widely used in the financial field for its characteristics of decentralization, anonymity and trust. Electronic money payment is an important application hotspot. Ring signature is widely used in strong...Block chain is widely used in the financial field for its characteristics of decentralization, anonymity and trust. Electronic money payment is an important application hotspot. Ring signature is widely used in strong anonymous authentication such as electronic cash and electronic voting because of its unconditional anonymity, spontaneity and flexible group structure. Among them, the correlation ring signature can prove whether two signatures are issued by the same person without revealing the identity of the real signer. Therefore, the signature right breach can be avoided based on the premise of guaranteeing anonymity, such as repeated voting, electronic money repetition cost and so on. Most of the existing correlation ring signature security is based on the discrete logarithm problem, and most of the schemes result in the degradation of anonymity because of strong association. These methods do not apply to the block chain electronic currency transaction scene with strong anonymity. Therefore, this paper first proposes a blockchain-based electronic currency transaction security model. The model ensures not only the anonymity of both parties but also a certain degree of traceability. In order to support these two characteristics, this paper proposes an association ring signature method based on large integer decomposition problem. This method has strong anonymity and can be applied to blockchain scenes. On the other hand, it can be converted into group signatures in specific scenarios. It is therefore traceable. Finally, the adaptive selection message of the scheme and the unforgeability under the selection of public key attack are proved under the random oracle model.展开更多
We introduce the concepts of left （right） zero-divisor rings, a class of rings without identity. We call a ring R left （right） zero-divisor if rR（a） ≠ 0（lR（a） ≠ 0） for every a∈ R, and call R strong left ...We introduce the concepts of left （right） zero-divisor rings, a class of rings without identity. We call a ring R left （right） zero-divisor if rR（a） ≠ 0（lR（a） ≠ 0） for every a∈ R, and call R strong left （right） zero-divisor if r R （R）≠0（lR（R）≠ 0）. Camillo and Nielson called a ring right finite annihilated （RFA） if every finite subset has non-zero right annihilator. We present in this paper some basic examples of left zero-divisor rings, and investigate the extensions of strong left zero-divisor rings and RFA rings, giving their equivalent characterizations.展开更多
We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and...We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.展开更多
Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relation...Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.展开更多
文摘This note is to investigate the properties of strongly semipotent rings.It is proved that every strongly semipotent ring is a idempotent unit regular ring,i.e.,there exist a non-zero idempotent e and a unit u such that er=eu for all r∉J(R),where J(R)is the Jacobson radical of ring R.
基金The Foundation for Excellent Doctoral Dissertationof Southeast University (NoYBJJ0507)the National Natural ScienceFoundation of China (No10571026)the Natural Science Foundation ofJiangsu Province (NoBK2005207)
文摘The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.
基金The National Natural Science Foundation of China(No.10971024)the Specialized Research Fund for the Doctoral Program of Higher Education(No.200802860024)the Natural Science Foundation of Jiangsu Province(No.BK2010393)
文摘An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.
文摘Let R be a ring and J（R） the Jacobson radical. An element a of R is called（strongly） J-clean if there is an idempotent e ∈ R and w ∈ J（R） such that a = e ＋ w（and ew = we）. The ring R is called a（strongly） J-clean ring provided that every one of its elements is（strongly） J-clean. We discuss, in the present paper,some properties of J-clean rings and strongly J-clean rings. Moreover, we investigate J-cleanness and strongly J-cleanness of generalized matrix rings. Some known results are also extended.
基金Supported by the Foundation for Young Talents in College of Anhui Province(Grant No.2012SQRL039ZD)the Postgraduate Innovation Foundation of Anhui University of Technology(Grant No.2014163)
文摘For a monoid M, we introduce the concept of skew strongly M-reversible rings which is a generalization of strongly M-reversible rings, and investigate their properties. It is shown that if G is a finitely generated Abelian group, then G is torsion-free if and only if there exists a ring R with 丨R丨 ≥ 2 such that R is skew strongly G-reversible. Moreover, we prove that if R is a right Ore ring with classical right quotient ring Q, then R is skew strongly M-reversible if and only if Q is skew strongly M-reversible.
基金Supported by the National Natural Science Foundation of China（11161006, 11171142） Supported by the Natural Science Foundation of Guangxi Province（2011GXNSFA018144, 018139, 2010GXNSFB 013048, 0991102）+2 种基金 Supported by the Guangxi New Century 1000 Talents Project Supported by the Guangxi Graduate Student Education Innovation Project（2011106030701M06） Supported by the SRF of Guangxi Education Committee
文摘In this paper we investigate strongly regular rings. In terms of W-ideals of rings some characterizations of strongly regular rings are given.
文摘?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.
基金partially supported by the Provincial Natural Science Foundation of Anhui Province of China（KJ2017A040）
文摘For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring Q, we prove that R is strongly M-α-reflexive if and only if Q is strongly M-α-reflexive, where R is α-rigid, α is an epimorphism of R. The relationship between some special subrings of upper triangular matrix rings and strongly M-α-reflexive rings is also investigated. Several known results similar to strongly M-α-reversible rings are obtained.
基金Supported by the Excellent Course Project for Postgraduates of Hunan University of Science and Technology(Grant No. J52112)
文摘We in this note introduce a new concept,so called strongly J-semiclean ring,that is a generalization of strongly J-clean rings.We first observe the basic properties of strongly J-semiclean rings,constructing typical examples.We next investigate conditions on a local ring R that imply that the upper triangular matrix ring Tn(R)is a strongly J-semiclean ring.Also,the criteria on strong J-semicleanness of 2×2 matrices in terms of a quadratic equation are given.As a consequence,several known results relating to strongly J-clean rings are extended to a more general setting.
基金Supported by National Natural Science Foundation of China(12301041)。
文摘In this paper,potent index of an element and pseudo clean rings are considered.Some properties and examples of pseudo clean rings are given.We also show that Zm is pseudo clean for every 2≤m∈Z and pseudo clean rings are clean.Furthermore,we prove pseudo clean rings are directly finite and have stable range one.
基金Supported by the NSF of Chinathe SFEM of China the Project of "Excellent Scholars Crossing the Centuries" of the Ministry of Education of China
文摘New kinds of strongly zero-dimensional locales are introduced and characterized, which are different from Johnstone's, and almost all the topological properties for strongly zero-dimensional spaces have the pointloss localic forms. Particularly. the Stone-Cech compactification of a strongly zero-diluensional locale is stongly zero-dimensional.
文摘A systematic study on ″ring phenomena″ frequently occurring before great earthquakes has made in this paper, which has analyzed the features of ring distributions before 16 great earthquakes and part of large earthquakes in China and its boundary areas, and discussed their features of generality, regularity and predictive meaning. The results have showed that moderate earthquakes or larger earthquakes distribute around the epicenter like a ring from decades to hundred years before the great earthquakes of magnitude more than 7, which is a general phenomenon of great earthquakes without an exception. The active ring generally occurs in the areas from hundreds to thousands of kilometers from the epicenter(according to the magnitude). The seismicity in the ring has three basic stages with different features. in the first stage, seismicity remains at low level and the earthquakes distribute scatteredly, while the source area of the future great earthquake remains quiet; in the second stage, the seismicity strengthens, whose frequency, intensity, concentrated degree, released rate of strain and ratio of distributed area etc. increase, while the quiet area decreases or disappears; in the third stage, the seismicity is weaker than in the former stage, and the quiet area appears again. The source area surrounded by the active ring might have three periods of activity(called as early term, medium term and late term foreshocks activity). The length of the quiet area undergoes the process from large to small, then to large. Therefore, we can estimate the occurring place, magnitude and seismogenic stage of great earthquake according to the area,length and the seismicity in the active ring, which is valuable to make a long term prediction of great earthquakes. At last, we had a preliminary discussion on the mechanism of active ring formation.
基金The National Natural Science Foundation （10571026） of China, and the Natural Science Foundation （BK2005207） of Jiangsu Province.
文摘A ring R is called left morphic, if for any a ∈ R, there exists b ∈ R such that lR（a） =Rb and lR（b）= Ra. In this paper, we use the method which is different from that of Lee and Zhou to investigate when R[x, σ]/（x^n） is （left） morphic and when the ideal extension E（R, V） is （left） morphic. It is mainly shown that： （1） If is an automorphism of a division ring R, then S = R[x, σ]/（x^n） （n 〉 1） is a special ring. （2） If d,m are positive integers and n = dm, then E（Zn, mZn） is a morphic ring if and only if gcd（d, m） = 1.
基金Supported by the National Natural Science Foundation of China(U1304614,U1204703)the Construct Program of the Key Discipline in Zhengzhou Normal UniversityAid Program for Science and Technology Innovative Research Team of Zhengzhou Normal University,Henan Province Education Science Plan General Topic((2018)-JKGHYB-0279)
文摘Block chain is widely used in the financial field for its characteristics of decentralization, anonymity and trust. Electronic money payment is an important application hotspot. Ring signature is widely used in strong anonymous authentication such as electronic cash and electronic voting because of its unconditional anonymity, spontaneity and flexible group structure. Among them, the correlation ring signature can prove whether two signatures are issued by the same person without revealing the identity of the real signer. Therefore, the signature right breach can be avoided based on the premise of guaranteeing anonymity, such as repeated voting, electronic money repetition cost and so on. Most of the existing correlation ring signature security is based on the discrete logarithm problem, and most of the schemes result in the degradation of anonymity because of strong association. These methods do not apply to the block chain electronic currency transaction scene with strong anonymity. Therefore, this paper first proposes a blockchain-based electronic currency transaction security model. The model ensures not only the anonymity of both parties but also a certain degree of traceability. In order to support these two characteristics, this paper proposes an association ring signature method based on large integer decomposition problem. This method has strong anonymity and can be applied to blockchain scenes. On the other hand, it can be converted into group signatures in specific scenarios. It is therefore traceable. Finally, the adaptive selection message of the scheme and the unforgeability under the selection of public key attack are proved under the random oracle model.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1107109711101217)
文摘We introduce the concepts of left （right） zero-divisor rings, a class of rings without identity. We call a ring R left （right） zero-divisor if rR（a） ≠ 0（lR（a） ≠ 0） for every a∈ R, and call R strong left （right） zero-divisor if r R （R）≠0（lR（R）≠ 0）. Camillo and Nielson called a ring right finite annihilated （RFA） if every finite subset has non-zero right annihilator. We present in this paper some basic examples of left zero-divisor rings, and investigate the extensions of strong left zero-divisor rings and RFA rings, giving their equivalent characterizations.
基金supported by the guidance project of scientific research plan of Educational Adminstration of Hubei Province,China(B2016162)the plan of science and technology innovation team of excellent young and middle-age of Hubei province(T201731)
文摘We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.
基金Foundation item:This work is partially supported by the NNSF(10171011)of Chinathe NNSF(10571026)of Chinathe Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutes of MOE,P.R.C.
文摘Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.
