Regular Elements of the Complete Semigroups <i>B<sub>X</sub>(D)</i>of Binary Relations of the Class ∑<sub>2</sub>(<i>X</i>,8)

• 作者: Nino Tsinaridze Shota Makharadze
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: SEMILATTICE Semigroup Binary Relation
• 年，卷（期）: 2015,（3）
• 页码范围: 447-455
• 页数: 9页
• 分类号: O1

摘要

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 .