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
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 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
By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (*,~)-relation H*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completel...By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (*,~)-relation H*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completely J*,^-simple semigroups. The result generalizes Petrich’s result on completely regular semigroups with Green’s relation H a normal band congruence or a regular band congruence from the round of regular semigroups to the round of r-ample semigroups.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
In order to obtain some results in the theory of semigroups, the concept of regularity, introduced by J. V. Neumann for elements of rings, is useful. In this work, all regular elements of semigroup defined by semilatt...In order to obtain some results in the theory of semigroups, the concept of regularity, introduced by J. V. Neumann for elements of rings, is useful. In this work, all regular elements of semigroup defined by semilattices of the class ∑<sub>1</sub>(X,10)-I are studied. When X has finitely many elements, we have given the number of regular elements.展开更多
In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a form...In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a formula for calculate idempotent and regular elements of BX (Q) defined by an X-semilattice of unions D.展开更多
In this paper we take subsemilattice of X-semilattice of unions D which satisfies the following conditions: We will investigate the properties of regular elements of the complete semigroup of binary relations Bx(D) sa...In this paper we take subsemilattice of X-semilattice of unions D which satisfies the following conditions: We will investigate the properties of regular elements of the complete semigroup of binary relations Bx(D) satisfying V(D,а)=Q. For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of regular elements and right units of the respective semigroup.展开更多
Sernirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent sernirings, and in particular, the variety of distributive lattices. Various st...Sernirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent sernirings, 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
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×∧Lambda L and ↓C(X,L) the one of the regions below of all continuou...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×∧Lambda L and ↓C(X,L) the one of the regions below of all continuous maps from X to ∧L. 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 ∧L is an AR, then USC(X,L) is homeomorphic to [-1,1]w. 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 thath_0= id USC (X, L) and ht( USC (X, L)(∪)↓ 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
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.
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.
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.
文摘By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (*,~)-relation H*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completely J*,^-simple semigroups. The result generalizes Petrich’s result on completely regular semigroups with Green’s relation H a normal band congruence or a regular band congruence from the round of regular semigroups to the round of r-ample semigroups.
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.
文摘In order to obtain some results in the theory of semigroups, the concept of regularity, introduced by J. V. Neumann for elements of rings, is useful. In this work, all regular elements of semigroup defined by semilattices of the class ∑<sub>1</sub>(X,10)-I are studied. When X has finitely many elements, we have given the number of regular elements.
文摘In this paper, we take Q16 subsemilattice of D and we will calculate the number of right unit, idempotent and regular elements α of BX (Q16) satisfied that V (D, α) = Q16 for a finite set X. Also we will give a formula for calculate idempotent and regular elements of BX (Q) defined by an X-semilattice of unions D.
文摘In this paper we take subsemilattice of X-semilattice of unions D which satisfies the following conditions: We will investigate the properties of regular elements of the complete semigroup of binary relations Bx(D) satisfying V(D,а)=Q. For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of regular elements and right units of the respective semigroup.
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Sernirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent sernirings, 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×∧Lambda L and ↓C(X,L) the one of the regions below of all continuous maps from X to ∧L. 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 ∧L is an AR, then USC(X,L) is homeomorphic to [-1,1]w. 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 thath_0= id USC (X, L) and ht( USC (X, L)(∪)↓ 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.
