Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on com...Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on completely regular semigroups.In this paper,we give one class of congruences on completely regular semigroups with the representation of wreath product of translational hulls on completely simple semigroups.By this new way,the least Clifford semigroup congruences on completely regular semigroups are generalized.展开更多
In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by nsing the equivalences on S/L, S/R and the special congruences on S. Also, such...In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by nsing the equivalences on S/L, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.展开更多
Let X be a Banach space with a weak uniform normal structure and C a non–empty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈...Let X be a Banach space with a weak uniform normal structure and C a non–empty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈? S} of selfmappings on C satisfying展开更多
Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-...Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p｜s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.展开更多
~*-regular semigroups may be regarded as algebras with the binary operation ofmultiplication and the unary operation of involution. They form a variety R~*,
This paper defines a kind of quasi-regular semigroups and the so-called E-ideal quasiregular semigroups and gives some of its characteristics and its two special cases (E-left regular quasi-regular semigroups, E-semil...This paper defines a kind of quasi-regular semigroups and the so-called E-ideal quasiregular semigroups and gives some of its characteristics and its two special cases (E-left regular quasi-regular semigroups, E-semilattice quasi-regular semigroups), thus estabishing a structure theorem for it, and as corollaries, obtaining a construction for a left regular band and the known construction for bands (Petrich, 1967).展开更多
In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （gener...In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.展开更多
The purpose of the paper is to characterize epigroups in which the idempotentgenerated subsemigroups are completely regular.Some special subclasses of the class of epigroups having the same property are also described.
The paper gives description of regular elements of the semigroup B X (D) which are defined by semilattices of the class Σ2 (X, 8), for which intersection the minimal elements is not empty. When X is a finite set, the...The paper gives description of regular elements of the semigroup B X (D) which are defined by semilattices of the class Σ2 (X, 8), for which intersection the minimal elements is not empty. When X is a finite set, the formulas are derived, by means of which the number of regular elements of the semigroup is calculated. In this case the set of all regular elements is a subsemigroup of the semigroup B X (D) which is defined by semilattices of the class Σ2 (X, 8).展开更多
Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a cong...Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?展开更多
A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semi...A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.展开更多
Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper. First, it is proved that this system possesses a unique global weak solution in H^1 （Ω, C ×R） by using ...Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper. First, it is proved that this system possesses a unique global weak solution in H^1 （Ω, C ×R） by using Galerkin method. Secondly, by using an iteration procedure, regularity estimates for the linear semigroups, it is proved that the model for liquid mixture of 3He-4He has a unique solution in H^k（Ω, C × R） for all k ≥ 1.展开更多
A left GC-lpp semigroup S is called split if the natural homomorphism γ^b of S onto S/γ induced by γ, is split. It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal. ...A left GC-lpp semigroup S is called split if the natural homomorphism γ^b of S onto S/γ induced by γ, is split. It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal. In particular, a construction theorem for split left GC-lpp semigroups is established.展开更多
This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contain...This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.展开更多
In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups...In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.展开更多
In this paper,we define intuitionistic fuzzy generalized bi-ideals in ordered semigroups and characterize regular and left weakly regular ordered semigroups in terms of intuitionistic fuzzy generalized bi-ideals.
基金National Natural Science Foundation of China(No.11671056)General Science Foundation of Shanghai Normal University,China(No.KF201840)。
文摘Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on completely regular semigroups.In this paper,we give one class of congruences on completely regular semigroups with the representation of wreath product of translational hulls on completely simple semigroups.By this new way,the least Clifford semigroup congruences on completely regular semigroups are generalized.
基金Supported by National Natural Science Foundation of China （Grant No. 10571061）
文摘In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by nsing the equivalences on S/L, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup.
基金supported both by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,P.R.C.by the National Natural Science Foundation 19801023
文摘Let X be a Banach space with a weak uniform normal structure and C a non–empty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈? S} of selfmappings on C satisfying
文摘Let S be a regular semigroup with an inverse transversal S° and C（S） the congruence lattice of S. A relation K° on C（S） is introduced as follows： if p, θ∈ C（S）, then we say that p and 0 are K°-related if Ker pO = Ker θ°, where p°= p｜s°. Expressions for the least and the greatest congruences in the same K°-class as p are provided. A number of equivalent conditions for K° being a congruence are given.
文摘~*-regular semigroups may be regarded as algebras with the binary operation ofmultiplication and the unary operation of involution. They form a variety R~*,
基金Project supported by the National Natural Science Foundation of China.
文摘This paper defines a kind of quasi-regular semigroups and the so-called E-ideal quasiregular semigroups and gives some of its characteristics and its two special cases (E-left regular quasi-regular semigroups, E-semilattice quasi-regular semigroups), thus estabishing a structure theorem for it, and as corollaries, obtaining a construction for a left regular band and the known construction for bands (Petrich, 1967).
基金The NSF(10961014) of Chinathe NSF(0501332) of Guangdong Province+1 种基金the Excellent Youth Talent Foundation(2009SQRZ149) of Anhui Provincethe Fuyang Normal College Youth Foundation (2008LQ11)
文摘In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.
基金Supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2010AL004)
文摘The purpose of the paper is to characterize epigroups in which the idempotentgenerated subsemigroups are completely regular.Some special subclasses of the class of epigroups having the same property are also described.
文摘The paper gives description of regular elements of the semigroup B X (D) which are defined by semilattices of the class Σ2 (X, 8), for which intersection the minimal elements is not empty. When X is a finite set, the formulas are derived, by means of which the number of regular elements of the semigroup is calculated. In this case the set of all regular elements is a subsemigroup of the semigroup B X (D) which is defined by semilattices of the class Σ2 (X, 8).
文摘Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?
文摘A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.
基金Sponsored by the National Natural Science Foundation of China(11071177)NSF of Sichuan Science and Technology Department of China(2010JY0057)the NSF of Sichuan Education Department of China(11ZA102)
文摘Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper. First, it is proved that this system possesses a unique global weak solution in H^1 （Ω, C ×R） by using Galerkin method. Secondly, by using an iteration procedure, regularity estimates for the linear semigroups, it is proved that the model for liquid mixture of 3He-4He has a unique solution in H^k（Ω, C × R） for all k ≥ 1.
基金Supported by the National Natural Science Foundation of China (Grant No. 10961014)the Natural Science Foundation of Jiangxi Provincethe Science Foundation of the Education Department of Jiangxi Province(Grant No. GJJ11388)
文摘A left GC-lpp semigroup S is called split if the natural homomorphism γ^b of S onto S/γ induced by γ, is split. It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal. In particular, a construction theorem for split left GC-lpp semigroups is established.
基金This project was supported by TRAPOYT, the Key Project of Chinese Ministry of Education(104126) the NNSF of China(10371046)
文摘This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.
基金Supported by the National Natural Science Foundation of China (Grant No. 10961014)the Science and Technology Projects in Guangdong Province (Grant No. 2010B010600039)+3 种基金the Guangdong Provincial Natural Science Foundation of China (Grant No. S2011010003681)the Anhui Provincial Excellent Youth Talent Foundation (Grant No. 2012SQRL115ZD)the University Natural Science Project of Anhui Province (Grant No. KJ2012B133)the Fuyang Normal College Natural Science Foundation (Grant No. 2007LZ01)
文摘In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.
文摘In this paper,we define intuitionistic fuzzy generalized bi-ideals in ordered semigroups and characterize regular and left weakly regular ordered semigroups in terms of intuitionistic fuzzy generalized bi-ideals.
