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
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
In this article, we study generated sets of the complete semigroups of binary relations defined by X-semilattices unions of the class Σ8 (X, n + k +1) , and find uniquely irreducible generating set for the given semi...In this article, we study generated sets of the complete semigroups of binary relations defined by X-semilattices unions of the class Σ8 (X, n + k +1) , and find uniquely irreducible generating set for the given semigroups.展开更多
In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive fo...In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.展开更多
In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive for...In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.展开更多
The main aim of the current research has been concentrated to clarify the condition for converting the inverse semigroups such as S to a semilattice. For this purpose a property the so-called has been de-fined and it ...The main aim of the current research has been concentrated to clarify the condition for converting the inverse semigroups such as S to a semilattice. For this purpose a property the so-called has been de-fined and it has been tried to prove that each inverse semigroups limited with show the specification of a semilattice.展开更多
In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of ...In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.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
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
Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and di...Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and different from the corresponding known results in the literature.Some special cases of the main result are also discussed.Some examples are given to illustrate the results.展开更多
In this paper, we explore the refined semilattice of left C-wrpp semigroups, and show that a left C-wrpp semigroup S is a refined semilattice of left-R cancellative stripes if and only if it is a spined product of a C...In this paper, we explore the refined semilattice of left C-wrpp semigroups, and show that a left C-wrpp semigroup S is a refined semilattice of left-R cancellative stripes if and only if it is a spined product of a C-wrpp component and a left regular band. It is a generalization of the refined semilattice decomposition of left C-rpp semigroups.展开更多
We prove that the adjoint semigroup of an implicative BCK algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK algebra with condition(s) is a generalized Boolean algebra. Moreover we prov...We prove that the adjoint semigroup of an implicative BCK algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK algebra with condition(s) is a generalized Boolean algebra. Moreover we prove the adjoint semigroup of a bounded implicative BCK algebra is a Boolean algebra.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.
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
In this paper, we show the existence of weak solutions for a higher order nonlinear elliptic equation. Our main method is to show that the evolution operator satisfies the fixed point theorem for Banach semilattice.
The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra from a Clifford monoid S =[Y; Gα. φα,β]by Ore-extensions, and to obtain a co-Frobenius semilat...The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra from a Clifford monoid S =[Y; Gα. φα,β]by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H（S, n, c, x, a, b） through factoring At by a semilattice graded weak Hopf ideal.展开更多
In this paper we study the closed subsemigroups of a Clifford semigroup. shown that{∪- αεY＇ Gα, [ Y＇ ε P（Y）} is the set of all closed subsemigroups of It is a Clifford semigroup S = {Y; Gα; Фα,β}, wher...In this paper we study the closed subsemigroups of a Clifford semigroup. shown that{∪- αεY＇ Gα, [ Y＇ ε P（Y）} is the set of all closed subsemigroups of It is a Clifford semigroup S = {Y; Gα; Фα,β}, where Y＇- denotes the suhsemilattice of Y generated by Y＇. In particular, G is the only dosed subsemigroup of itself for a group G and each one of subsemilattiees of a semilattiee is closed. Also, it is shown that the semiring P（S） is isomorphic to the semiring P（Y） for a Clifford semigroup S = [Y; Gα; Фα,β].展开更多
The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from...The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.展开更多
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.
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In this article, we study generated sets of the complete semigroups of binary relations defined by X-semilattices unions of the class Σ8 (X, n + k +1) , and find uniquely irreducible generating set for the given semigroups.
文摘In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.
文摘In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.
文摘The main aim of the current research has been concentrated to clarify the condition for converting the inverse semigroups such as S to a semilattice. For this purpose a property the so-called has been de-fined and it has been tried to prove that each inverse semigroups limited with show the specification of a semilattice.
文摘In this paper we give a full description of idempotent elements of the semigroup BX (D), which are defined by semilattices of the class ∑1 (X, 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.
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.
基金partially supported by NAFOSTED under Grant No.101.01-2014.17UTC under Grant No.T2017-KHCB-60
文摘Under new assumptions,this paper obtains some extended versions of Ky Fan type inequality for a family of C-continuous set-valued mappings in the setting of topological semilattices.The obtained results are new and different from the corresponding known results in the literature.Some special cases of the main result are also discussed.Some examples are given to illustrate the results.
基金the Natural Science Foundation of Huizhou University （No. C207.0202）.
文摘In this paper, we explore the refined semilattice of left C-wrpp semigroups, and show that a left C-wrpp semigroup S is a refined semilattice of left-R cancellative stripes if and only if it is a spined product of a C-wrpp component and a left regular band. It is a generalization of the refined semilattice decomposition of left C-rpp semigroups.
文摘We prove that the adjoint semigroup of an implicative BCK algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK algebra with condition(s) is a generalized Boolean algebra. Moreover we prove the adjoint semigroup of a bounded implicative BCK algebra is a Boolean algebra.
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.
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 .
基金The Key Project of Jilin University of Finance and Economics(2018Z02)the NSF(11701209)of China
文摘In this paper, we show the existence of weak solutions for a higher order nonlinear elliptic equation. Our main method is to show that the evolution operator satisfies the fixed point theorem for Banach semilattice.
基金supported by the National Natural Science Foundation of China(11271318,11171296,and J1210038)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20110101110010)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010001)
文摘The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra from a Clifford monoid S =[Y; Gα. φα,β]by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H（S, n, c, x, a, b） through factoring At by a semilattice graded weak Hopf ideal.
文摘In this paper we study the closed subsemigroups of a Clifford semigroup. shown that{∪- αεY＇ Gα, [ Y＇ ε P（Y）} is the set of all closed subsemigroups of It is a Clifford semigroup S = {Y; Gα; Фα,β}, where Y＇- denotes the suhsemilattice of Y generated by Y＇. In particular, G is the only dosed subsemigroup of itself for a group G and each one of subsemilattiees of a semilattiee is closed. Also, it is shown that the semiring P（S） is isomorphic to the semiring P（Y） for a Clifford semigroup S = [Y; Gα; Фα,β].
文摘The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.
