Generating Sets of the Complete Semigroup of Binary Relations Defined by Semilattices of the Class Σ8(X, 5)

In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ8(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.

(Generalized)Green's Relations of GV-Semigroups

Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.

SOME REMARKS ON (L)-GREEN’S RELATIONS AND STRONGLY RPP SEMIGROUPS

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.

Regular Elements of the Complete Semigroups <i>B_X(D)</i>of Binary Relations of the Class &sum;₂(<i>X</i>,8)

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 .

A Class of Regular Simple ω2-semigroups-Ⅱ

In this paper, we study regular simple ω2-semigroups in which D｜Es = Wd by the generalized Bruck-Reilly extension and obtain its structure theorem.

Generating Set of the Complete Semigroups of Binary Relations

Difficulties encountered in studying generators of semigroup of binary relations defined by a complete X -semilattice of unions D arise because of the fact that they are not regular as a rule, which makes their investigation problematic. In this work, for special D, it has been seen that the semigroup , which are defined by semilattice D, can be generated by the set .

Generated Sets of the Complete Semigroup Binary Relations Defined by Semilattices of the Class Σ₈(<em>X</em>, <em>n</em>+ <em>k</em>+ 1)

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.

A Class of ＊-simple Type A ω~2 -semigroups （Ⅰ）

In this paper, we study ＊-simple type A ω2 -semigroups in which D＊= D and D＊｜ES = Md by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two such semigroups.

On Commutative Δ-Semigroups

In this paper entitled on commutative Delta-Semigroups, we have obtained important results on commutative Δ-semigroups.

Generating Sets of the Complete Semigroups of Binary Relations Defined by Semilattices of the Class Σ_(2)(X,4)

In this paper, we have studied generating sets of the complete semigroups defined by X-semilattices of the class Σ2(X, 4).

Complete Semigroups of Binary Relations Defined by Semilattices of the Class Σ_(1)(X,10)

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.

Idempotent and Regular Elements of the Complete Semigroups of Binary Relations of the Class Σ_(3)(X,9)

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.

保持等价关系的变换半群的一些结果

给出了保持等价关系的变换半群上的格林关系L,R,H和格林*-关系L^(*),R^(*),H^(*)相容的充要条件,刻画了这类半群的左(右,完全)正则性,得到了这类半群的全体幂等元(正则元,富足元)构成子半群的等价描述.

On Some Subsemigroups of the 4-cyclic Semigroup-Ⅱ

In this paper, we study subsemigroups Bd,o of the 4-cyclic semigroup Bω2 and characterize the Green＇s relations of Bd,o. We show that, up to isomorphism, the only fundamental simple inverse w2-semigroups such that D│E（s） =Md are the semigroupsBd,o（d = 1, 2, 3,... ）.

Regular Elements of the Semigroup <i>B</i>_X(<i>D</i>) Defined by Semilattices of the Class &Sigma;₂(<i>X</i>, 8) and Their Calculation Formulas

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).

Idempotent Elements of the Semigroups BX(D) Defined by Semilattices of the Class ∑3 (X,8) When Z7=Ø

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.

Idempotent Elements of the Semigroups Bx(D) Defined by Semilattices of the Class ∑3(x,8) When Z7‡Ø

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.

半群PO_(n)(k)的格林(星)关系及富足性

设P_(n)和PO_(n)分别是有限链[n]上的部分变换半群和保序部分变换半群.对任意1≤k≤n,令PO_(n)(k)={α∈PO_(n)(k):■x∈dom(α),x≤k■xα≤k},则PO_(n)(k)是P_(n)的子半群.通过分析半群PO_(n)(k)中的元素,获得了半群PO_(n)(k)的格林关系和格林星关系.进一步讨论了:当1≤k≤n-1时,半群PO_(n)(k)是非正则富足半群.

半群O_(n)^([l,m])的格林(星)关系及富足性

设O_(n)是有限链X_(n)上的保序变换半群,对任意1≤l≤m≤n,令O_(n)^([l,m])={α∈O_(n):∀x∈X_(n),l≤xα≤m},易证半群O_(n)^([l,m])是O_(n)的子半群,刻画了半群O_(n)^([l,m])的格林关系和正则元的特征,进一步获得了半群O_(n)^([l,m])的星格林关系及非正则富足性.

半群上的L-模糊同余

半群S上的模糊关系是特殊的映射,它将S×S映到[0,1]区间。[0,1]区间是全序集,是特殊的格。通过将[0,1]换成完全格推广模糊关系的定义得到L-模糊关系的定义。在此基础上给出L-模糊等价关系、L-模糊同余的定义。研究了半群S上的L-模糊同余的部分性质,证明了两个L-模糊同余他们的圈乘是L-模糊同余当且仅当他们的圈乘是L-模糊等价关系当且仅当他们的圈乘是L-模糊对称的当且仅当他们的圈乘满足交换律。最终证明了μ^(-1)(1)={(a,b)∈S×S|μ(a,b)=1}是半群S上的同余。