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Regular Elements of the Complete Semigroups BX(D)of Binary Relations of the Class ∑2(X,8)

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Applied Mathematics 2015年第3期6卷 447-455页

作者： nino tsinaridze Shota Makharadze Department of Mathematics Faculty of Mathematics Physics and Computer Sciences Shota Rustaveli Batumi State University Batumi Georgia

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 .

关键词： Semilattice Semigroup Binary Relation

Regular Elements of the Semigroup BX (D) Defined by Semilattices of the Class Σ2(X, 8) and Their Calculation Formulas

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Applied Mathematics 2015年第14期6卷 2257-2278页

作者： nino tsinaridze Shota Makharadze Guladi Fartenadze Department of Mathematics Faculty of Physics Mathematics and Computer Sciences Shota Rustaveli Batumi State University Batumi Georgia

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).

关键词： Semilattice Semigroup Binary Relation Regular Element

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

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Applied Mathematics 2018年第4期9卷 369-382页

作者： Yasha Diasamidze Omari Givradze nino tsinaridze Giuli Tavdgiridze Faculty of Mathematics Physics and Computer Sciences Shota Rustaveli State University Batumi Georgia

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... 详细信息

关键词： Semigroup Semilattice Binary Relation

Regular Elements of B_X (D) Defined by the Class ∑₁(X,10)-Ⅱ

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Applied Mathematics 2016年第9期7卷 894-907页

作者： Yasha Diasamidze nino tsinaridze Neşet Aydn Ali Erdoğan Shota Rustavelli University Batumi Georgia Ç anakkale Onsekiz Mart University &Ccedil anakkale Turkey Hacettepe University Ankara Turkey

This part of the paper is the continuotion of paper “Regular Elements of BX (D) Defined by the Class ∑1(X,10)-Ⅰ”.

关键词： Semilattice Semigroup Binary Relation

Regular Elements of B_{x(D) Defined by the Class ∑₁(X,10)-I}

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Applied Mathematics 2016年第9期7卷 867-893页

作者： Yasha Diasamidze nino tsinaridze Neşet Aydn Neşet Aydn Ali Erdoğan Shota Rustavelli University Batumi Georgia Ç anakkale Onsekiz Mart University &Ccedil anakkale Turkey Hacettepe University Ankara Turkey

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 ∑1(X,10)-I are studied. When X has finitely many elements, we have given the number of regular elements.

关键词： Semilattice Semigroup Binary Relation