## Regular elements of the complete semigroups of binary relations of the class Sigma(6)(X, 8)

GEORGIAN MATHEMATICAL JOURNAL, vol.22, no.2, pp.159-170, 2015 (Peer-Reviewed Journal)  • Publication Type: Article / Article
• Volume: 22 Issue: 2
• Publication Date: 2015
• Doi Number: 10.1515/gmj-2015-0009
• Journal Name: GEORGIAN MATHEMATICAL JOURNAL
• Journal Indexes: Science Citation Index Expanded, Scopus
• Page Numbers: pp.159-170

#### Abstract

In this paper, let X be a finite set, D be a complete X-semilattice of unions and Q = {T-1, T-2, T-3, T-4, T-5, T-6, T-7, T-8} be an X-subsemilattice of D where T-1 subset of T-3 subset of T-5 subset of T-6 subset of T-8, T-1 subset of T-3 subset of T-5 subset of T-7 subset of T-8, T-2 subset of T-3 subset of T-5 subset of T-6 subset of T-8, T-2 subset of T-3 subset of T-5 subset of T-7 subset of T-8, T-2 subset of T-4 subset of T-5 subset of T-6 subset of T-8, T-2 subset of T-4 subset of T-5 subset of T-7 subset of T-8, T-2 \ T-1 not equal empty set, T-1 \ T-2 not equal empty set, T4 \ T-3 not equal empty set, T-3 \ T-4 not equal empty set, T-6 \ T-7 not equal empty set, T-7 \ T-6 not equal empty set, T-2 boolean OR T-1 = T-3, T-4 boolean OR T-3 = T-5, T-6 boolean OR T-7 = T-8. Using the characteristic family of sets, the characteristic mapping and base sources of Q, we characterize the class whose elements are each isomorphic to Q. We generate some advanced formulas in order to calculate the number of regular elements alpha of B-X (D) satisfying V (D, alpha) = Q, in an efficient way.