Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous m...Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous maps from X to AL. USC(X, L) with the Vietoris topology is a topological space and ↓C(X, L) is its subspace. It will be proved that, if X is an infinite locally connected compactum and AL is an AR, then USC(X, L) is homeomorphic to [-1,1]ω. Furthermore, if L is the product of countably many intervals, then ↓ C(X, L) is homotopy dense in USC(X,L), that is, there exists a homotopy h : USC(X,L) × [0,1] →USC(X,L) such that h0 = idUSC(X,L) and ht(USC(X,L)) C↓C(X,L) for any t > 0. But ↓C(X, L) is not completely metrizable.展开更多
As generalization of Clifford semigroups, left Clifford semigroups are defined and ξ-products for such semigroups and their semilattice decompositions are studied. In particular, considering how a semilattice decompo...As generalization of Clifford semigroups, left Clifford semigroups are defined and ξ-products for such semigroups and their semilattice decompositions are studied. In particular, considering how a semilattice decomposition becomes a strong semilattice decomposition and ξ-product becomes spined product, some structure theorems and characteristics for this class of semigroups are obtained.展开更多
In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for...In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for the given semigroups and when X is finite set formulas for calculating the number of elements in generating sets are derived.展开更多
We define orthodox super rpp semigroups and study their semilattice decompositions. Standard representation theorem of orthodox super rpp semigroups whose subband of idempotents is in the varieties of bands described ...We define orthodox super rpp semigroups and study their semilattice decompositions. Standard representation theorem of orthodox super rpp semigroups whose subband of idempotents is in the varieties of bands described by an identity with at most three variables are obtained.展开更多
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
Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal（right ideal,bi-ideal） is an ordered subsemigroup（resp.,ideal,right ideal,left ideal,bi-ideal,interi...Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal（right ideal,bi-ideal） is an ordered subsemigroup（resp.,ideal,right ideal,left ideal,bi-ideal,interior ideal） by using some binary relations on S.展开更多
Semirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent semirings, and in particular, the variety of distributive lattices. Various stru...Semirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent semirings, and in particular, the variety of distributive lattices. Various structure theorems are established which bring insight into the structure of the lattice of subvarieties of S.展开更多
Suda （2012） extended the ErdSs-Ko-Rado theorem to designs in strongly regularized semilattices. In this paper we generalize Suda＇s results in regularized semilattices and partition regularized semilattices, give ma...Suda （2012） extended the ErdSs-Ko-Rado theorem to designs in strongly regularized semilattices. In this paper we generalize Suda＇s results in regularized semilattices and partition regularized semilattices, give many examples for these semilattices and obtain their intersection theorems.展开更多
In order to study rpp semigroups, in particular, some special cases, several facts on （l）-Green’s relations and strongly rpp semigroups are given as some remarks.
Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R（A1, S）, where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T（J（S）） which is obtained from the ...Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R（A1, S）, where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T（J（S）） which is obtained from the Jordan algebra ,：7（S） by the so-called Tits-Kantor-Koecher construction. In this article we consider the Zn-graded automorphism group of the TKK Lie algebra T（J（S））, where S is the ＂smallest＂ semilattice in Euclidean space Rn.展开更多
As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) ...As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q∈∑2(X,8) . Because the semilattice Q of the class ∑2(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q .展开更多
We define the right regular dual of an object X in a monoidal category l, and give several results regarding the weak rigid monoidal category. Based on the definition of the right regular dual, we construct a weak Hop...We define the right regular dual of an object X in a monoidal category l, and give several results regarding the weak rigid monoidal category. Based on the definition of the right regular dual, we construct a weak Hopf algebra structure of H = End（F） whenever （F, J） is a fiber functor from category l to Vec and every X ∈ l has a right regular dual. To conclude, we give a weak reconstruction theorem for a kind of weak Hopf algebra.展开更多
In handing information regarding various aspects of uncertainty, non-classical-mathematics (fuzzy mathematics or great extension and development of classical mathematics) is considered to be a more powerful technique ...In handing information regarding various aspects of uncertainty, non-classical-mathematics (fuzzy mathematics or great extension and development of classical mathematics) is considered to be a more powerful technique than classical mathematics. The non-classical mathematics, therefore, has now days become a useful tool in applications mathematics and computer science. The purpose of this paper is to apply the concept of the fuzzy sets to some algebraic structures such as an ideal, upper semilattice, lower semilattice, lattice and sub-algebra and gives some properties of these algebraic structures by using the concept of fuzzy sets. Finally, related properties are investigated in fuzzy BCK-algebras.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.10471084)by Guangdong Provincial Natural Science Fundation(Grant No.04010985).
文摘Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous maps from X to AL. USC(X, L) with the Vietoris topology is a topological space and ↓C(X, L) is its subspace. It will be proved that, if X is an infinite locally connected compactum and AL is an AR, then USC(X, L) is homeomorphic to [-1,1]ω. Furthermore, if L is the product of countably many intervals, then ↓ C(X, L) is homotopy dense in USC(X,L), that is, there exists a homotopy h : USC(X,L) × [0,1] →USC(X,L) such that h0 = idUSC(X,L) and ht(USC(X,L)) C↓C(X,L) for any t > 0. But ↓C(X, L) is not completely metrizable.
基金Proiect supported by the National Natural science Founnation of China
文摘As generalization of Clifford semigroups, left Clifford semigroups are defined and ξ-products for such semigroups and their semilattice decompositions are studied. In particular, considering how a semilattice decomposition becomes a strong semilattice decomposition and ξ-product becomes spined product, some structure theorems and characteristics for this class of semigroups are obtained.
文摘In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for the given semigroups and when X is finite set formulas for calculating the number of elements in generating sets are derived.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071068)a Youth Scientific Foundation grant of Hunan Education Department(Grant No.02B024)a UGC(HK)(Grant No.2060187(02/04)).
文摘We define orthodox super rpp semigroups and study their semilattice decompositions. Standard representation theorem of orthodox super rpp semigroups whose subband of idempotents is in the varieties of bands described by an identity with at most three variables are obtained.
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Supported by the National Natural Science Foundation of China (Grant No.10961014)the Natural Science Foundation of Guangdong Province (Grant No.0501332)+1 种基金the Excellent Youth Talent Foundation of Anhui Province(Grant No.2009SQRZ149)the Youth Foundation of Fuyang Normal College (Grant No.2008LQ11)
文摘Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal（right ideal,bi-ideal） is an ordered subsemigroup（resp.,ideal,right ideal,left ideal,bi-ideal,interior ideal） by using some binary relations on S.
基金Guo Yuqi was supported by the National Natural Science Foundation of China (Grant No. 10071068) the Provincial Applied Fundamental Research Foundation of Yunnan Province of China.
文摘Semirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent semirings, and in particular, the variety of distributive lattices. Various structure theorems are established which bring insight into the structure of the lattice of subvarieties of S.
基金supported by National Natural Science Foundation of China(Grant Nos.11271047 and 10971052)Natural Science Foundation of Hebei Province(Grant Nos.A2012408003 and A2012205079)+3 种基金the Talent Project Fund of Hebei Province(Grant No.2011-11)the Doctoral Fund from Hebei Normal University(Grant No.L2011B02)Scientific Research Fund of the Department of Education of Hebei Education Department(Grant No.ZH2012082)the Fundamental Research Funds for the Central University of China
文摘Suda （2012） extended the ErdSs-Ko-Rado theorem to designs in strongly regularized semilattices. In this paper we generalize Suda＇s results in regularized semilattices and partition regularized semilattices, give many examples for these semilattices and obtain their intersection theorems.
基金The research of the second author was supported by the NSFC (10871161)
文摘In order to study rpp semigroups, in particular, some special cases, several facts on （l）-Green’s relations and strongly rpp semigroups are given as some remarks.
基金Supported by National Natural Science Foundation of China （Grant No. 10931006） and Foundation of Educational Department of Hubei Province in China （Grant No. B200529001） The author is grateful to the referee for some helpful suggestions.
文摘Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R（A1, S）, where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T（J（S）） which is obtained from the Jordan algebra ,：7（S） by the so-called Tits-Kantor-Koecher construction. In this article we consider the Zn-graded automorphism group of the TKK Lie algebra T（J（S））, where S is the ＂smallest＂ semilattice in Euclidean space Rn.
文摘As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q∈∑2(X,8) . Because the semilattice Q of the class ∑2(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q .
文摘We define the right regular dual of an object X in a monoidal category l, and give several results regarding the weak rigid monoidal category. Based on the definition of the right regular dual, we construct a weak Hopf algebra structure of H = End（F） whenever （F, J） is a fiber functor from category l to Vec and every X ∈ l has a right regular dual. To conclude, we give a weak reconstruction theorem for a kind of weak Hopf algebra.
文摘In handing information regarding various aspects of uncertainty, non-classical-mathematics (fuzzy mathematics or great extension and development of classical mathematics) is considered to be a more powerful technique than classical mathematics. The non-classical mathematics, therefore, has now days become a useful tool in applications mathematics and computer science. The purpose of this paper is to apply the concept of the fuzzy sets to some algebraic structures such as an ideal, upper semilattice, lower semilattice, lattice and sub-algebra and gives some properties of these algebraic structures by using the concept of fuzzy sets. Finally, related properties are investigated in fuzzy BCK-algebras.
