In this paper, we describe all the divisible semiring congruences on a distributive semiring S and also establish a one_to_one, inclusion_preserving mapping from the set of full, closed, self_conjagate, ideal subsemir...In this paper, we describe all the divisible semiring congruences on a distributive semiring S and also establish a one_to_one, inclusion_preserving mapping from the set of full, closed, self_conjagate, ideal subsemirings of S to the set of all divisible semiring congruences on S.展开更多
The idempotent semirings Rmax and Rmin play a crucial role in several areas of mathematics and their applications such as discrete mathematics, algebraic geometry, computer science, computer languages, linguistic prob...The idempotent semirings Rmax and Rmin play a crucial role in several areas of mathematics and their applications such as discrete mathematics, algebraic geometry, computer science, computer languages, linguistic problems, optimization theory, discrete event systems, fuzzy logics. In this paper we consider the expansion of the semirings Rmax and Rmin with residuals and describe how to use these expended semirings in public key cryptography.展开更多
The investigation of congruences on generalized inverse semigroups is initiated. Following some properties of such semigroups, the congruences on an orthodox semiring whose idempotents satisfy permutation identities a...The investigation of congruences on generalized inverse semigroups is initiated. Following some properties of such semigroups, the congruences on an orthodox semiring whose idempotents satisfy permutation identities are established. In addition, we give a structure theorem of homomorphic image of this kind of orthodox semirings.展开更多
On the basis of concepts of bipolar fuzzy sets, we establish a new framework of bipolar fuzzy subsemirings（resp., ideals） which is a generalization of traditional fuzzy subsemirings（resp., ideals） in semirings. Th...On the basis of concepts of bipolar fuzzy sets, we establish a new framework of bipolar fuzzy subsemirings（resp., ideals） which is a generalization of traditional fuzzy subsemirings（resp., ideals） in semirings. The concepts of bipolar fuzzy subsemirings（resp., ideals） are introduced and related properties are investigated by means of positive t-cut, negative s-cut and equivalence relation. Particularly, the notion of a normal bipolar fuzzy ideal is given, and some basic properties are studied in this paper.展开更多
In this paper, we discussed the property of rectangular band semiring congruence and ring congruence on a semiring and gave some characterizations and structure of rectangular ring congruence on an E-inversive semiring.
This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplicat...This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplication operator semigroup of semiring semigroup.展开更多
Let V be the variety generated by two-element distributive lattice B2 and k prime fields Fp1,...,Fpk. That is to say that V = HSP{B2, Fp1,...,Fpk}. It is proved that the variety V is finitely based. Also, the two-elem...Let V be the variety generated by two-element distributive lattice B2 and k prime fields Fp1,...,Fpk. That is to say that V = HSP{B2, Fp1,...,Fpk}. It is proved that the variety V is finitely based. Also, the two-element distributive lattice B2 and prime fields Fp1,..., Fpk are, up to isomorphism, the only subdirectly irreducible semirings in V. Some known results are extended and enriched.展开更多
Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrice...Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrices in Mn（S） if for any A ∈ Mn（S）, A is nilpotent if and only if L（A） is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.展开更多
In this paper, we define the fuzzy k_i deal as a new fuzzification of the k_ideal in a semiring. Also we study the properties of the image and inverse image of a fuzzy k_ideal in a se miring under homomorphism. For e...In this paper, we define the fuzzy k_i deal as a new fuzzification of the k_ideal in a semiring. Also we study the properties of the image and inverse image of a fuzzy k_ideal in a se miring under homomorphism. For example, the fuzzy k_ideal in the nonnegative integers semiring N is given.展开更多
In this paper,the semirings with invariant basis numbers are investigated.First,we give some properties of a semiring which has an invariant basis number,and then give some necessary and sufcient conditions that the d...In this paper,the semirings with invariant basis numbers are investigated.First,we give some properties of a semiring which has an invariant basis number,and then give some necessary and sufcient conditions that the direct sum of two semirings has an invariant basis number.As an application,we prove that division semirings,quasilocal semirings and stably fnite semirings have invariant basis numbers,respectively.展开更多
This paper deals with orthodox semirings whose additive idempotents satisfy permutation identities. A structure theorem for such semirings is established.
On completely regular semirings,we give alternative characterizations for the kernel of a congruence and idempotent pure congruences.Then we give alternative characterizations for the trace of a congruence and idempot...On completely regular semirings,we give alternative characterizations for the kernel of a congruence and idempotent pure congruences.Then we give alternative characterizations for the trace of a congruence and idempotent separating congruences.In addition,we conclude that a congruence is uniquely determined by its kernel and trace.展开更多
In this paper, we generalize Clifford semirings to left Clifford semirings bymeans of the so-called band semirings. We also discuss a special case of this kind of semirings,that is, strong distributive lattices of lef...In this paper, we generalize Clifford semirings to left Clifford semirings bymeans of the so-called band semirings. We also discuss a special case of this kind of semirings,that is, strong distributive lattices of left rings.展开更多
Let S be an antinegative commutative semiring having no zero divisions or finite general Boolean Algebra and μ(S) the set of n×n matrices over S. In this paper we characterize the structure of the senigroup n,...Let S be an antinegative commutative semiring having no zero divisions or finite general Boolean Algebra and μ(S) the set of n×n matrices over S. In this paper we characterize the structure of the senigroup n,(S) of linear operators on μn,(S) that strongly preserve the M-P inverses of matrices.展开更多
Let D be an integral domain,F^(+)(D)(resp.,f^(+)(D))be the set of nonzero(resp.,nonzero finitely generated)ideals of D,R_(1)=f+(D)∪{(0)},and R_(2)=F+(D)∪{(0)}.Then(R_(i),㊉,■)for i=1,2 is a commutative semiring wit...Let D be an integral domain,F^(+)(D)(resp.,f^(+)(D))be the set of nonzero(resp.,nonzero finitely generated)ideals of D,R_(1)=f+(D)∪{(0)},and R_(2)=F+(D)∪{(0)}.Then(R_(i),㊉,■)for i=1,2 is a commutative semiring with identity under I㊉J=I+J and I■J=ZJ for all I,J∈R_(i).In this paper,among other things,we show that D is a Priifer domain if and only if every ideal of R_(1)is a k-ideal if and only if R_(1)is Gaussian.We also show that D is a Dedekind domain if and only if R_(2)is a unique factorization semidomain if and only if R_(2)is a principal ideal semidomain.These results are proved in a more general setting of star operations on D.展开更多
An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal idea...An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring.展开更多
A solution is given for the word problem for free idempotent distributive semirings. Using this solution the lattice L(ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns...A solution is given for the word problem for free idempotent distributive semirings. Using this solution the lattice L(ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out that L(ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four copies of the lattice L (B) of all band varieties. Therefore L(ID) is countably infinite and distributive. Every subvariety of ID is finitely based.展开更多
文摘In this paper, we describe all the divisible semiring congruences on a distributive semiring S and also establish a one_to_one, inclusion_preserving mapping from the set of full, closed, self_conjagate, ideal subsemirings of S to the set of all divisible semiring congruences on S.
文摘The idempotent semirings Rmax and Rmin play a crucial role in several areas of mathematics and their applications such as discrete mathematics, algebraic geometry, computer science, computer languages, linguistic problems, optimization theory, discrete event systems, fuzzy logics. In this paper we consider the expansion of the semirings Rmax and Rmin with residuals and describe how to use these expended semirings in public key cryptography.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1096101411101354)+1 种基金the Natural Science Foundation of Jiangxi Provincethe Science Foundation of the Education Department of Jiangxi Province
文摘The investigation of congruences on generalized inverse semigroups is initiated. Following some properties of such semigroups, the congruences on an orthodox semiring whose idempotents satisfy permutation identities are established. In addition, we give a structure theorem of homomorphic image of this kind of orthodox semirings.
基金Supported by the National Natural Science Foundation of China (Grant No.11071151)
文摘On the basis of concepts of bipolar fuzzy sets, we establish a new framework of bipolar fuzzy subsemirings（resp., ideals） which is a generalization of traditional fuzzy subsemirings（resp., ideals） in semirings. The concepts of bipolar fuzzy subsemirings（resp., ideals） are introduced and related properties are investigated by means of positive t-cut, negative s-cut and equivalence relation. Particularly, the notion of a normal bipolar fuzzy ideal is given, and some basic properties are studied in this paper.
基金Supported by the National Natural Science Foundation of China（10961014,11101354） Supported by the Natural Science Foundation of Jiangxi Province（0611051） Supported by the Science Foundation of the Education Department of Jiangxi Province（GJ 09459）
文摘In this paper, we discussed the property of rectangular band semiring congruence and ring congruence on a semiring and gave some characterizations and structure of rectangular ring congruence on an E-inversive semiring.
文摘This paper characterizes the multiplication operator semigroup of semiring semigroup by using the tensor product of semigroups, and by using the endomorphism semigroup, and considers some properties of the multiplication operator semigroup of semiring semigroup.
基金China Postdoctoral Science Foundation(Grant No.2011M501466)the Natural Science Foundation of Shannxi Province(Grant No.2011JQ1017)
文摘Let V be the variety generated by two-element distributive lattice B2 and k prime fields Fp1,...,Fpk. That is to say that V = HSP{B2, Fp1,...,Fpk}. It is proved that the variety V is finitely based. Also, the two-element distributive lattice B2 and prime fields Fp1,..., Fpk are, up to isomorphism, the only subdirectly irreducible semirings in V. Some known results are extended and enriched.
文摘Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrices in Mn（S） if for any A ∈ Mn（S）, A is nilpotent if and only if L（A） is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.
文摘In this paper, we define the fuzzy k_i deal as a new fuzzification of the k_ideal in a semiring. Also we study the properties of the image and inverse image of a fuzzy k_ideal in a se miring under homomorphism. For example, the fuzzy k_ideal in the nonnegative integers semiring N is given.
基金Sichuan Nature Science Fund for Distinguished Young Scholars(Grant No.2025NSFJQ0048)。
文摘In this paper,the semirings with invariant basis numbers are investigated.First,we give some properties of a semiring which has an invariant basis number,and then give some necessary and sufcient conditions that the direct sum of two semirings has an invariant basis number.As an application,we prove that division semirings,quasilocal semirings and stably fnite semirings have invariant basis numbers,respectively.
文摘This paper deals with orthodox semirings whose additive idempotents satisfy permutation identities. A structure theorem for such semirings is established.
基金Natural Science Foundation of China(11971383,11801239)Shaanxi Fundamental Science Research Project for Mathematics and Physics(22JSY023).
文摘On completely regular semirings,we give alternative characterizations for the kernel of a congruence and idempotent pure congruences.Then we give alternative characterizations for the trace of a congruence and idempotent separating congruences.In addition,we conclude that a congruence is uniquely determined by its kernel and trace.
文摘In this paper, we generalize Clifford semirings to left Clifford semirings bymeans of the so-called band semirings. We also discuss a special case of this kind of semirings,that is, strong distributive lattices of left rings.
文摘Let S be an antinegative commutative semiring having no zero divisions or finite general Boolean Algebra and μ(S) the set of n×n matrices over S. In this paper we characterize the structure of the senigroup n,(S) of linear operators on μn,(S) that strongly preserve the M-P inverses of matrices.
基金supported by the Incheon National University Research Grant in 2018(Grant No.2018-0014).
文摘Let D be an integral domain,F^(+)(D)(resp.,f^(+)(D))be the set of nonzero(resp.,nonzero finitely generated)ideals of D,R_(1)=f+(D)∪{(0)},and R_(2)=F+(D)∪{(0)}.Then(R_(i),㊉,■)for i=1,2 is a commutative semiring with identity under I㊉J=I+J and I■J=ZJ for all I,J∈R_(i).In this paper,among other things,we show that D is a Priifer domain if and only if every ideal of R_(1)is a k-ideal if and only if R_(1)is Gaussian.We also show that D is a Dedekind domain if and only if R_(2)is a unique factorization semidomain if and only if R_(2)is a principal ideal semidomain.These results are proved in a more general setting of star operations on D.
基金Supported by the National Natural Science Foundation of Jiangxi Province (Grant No.2010GZS0093)
文摘An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring.
基金Project supported by the National Natural Science Foundation of China (Grant No. 197610O4)the Provincial Applied Fundamental Research Foundation of Yunnan (96a001z).
文摘A solution is given for the word problem for free idempotent distributive semirings. Using this solution the lattice L(ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out that L(ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four copies of the lattice L (B) of all band varieties. Therefore L(ID) is countably infinite and distributive. Every subvariety of ID is finitely based.
