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    Öğe
    Regular elements of the complete semigroups of binary relations of the class ?6(X, 8)
    (Walter De Gruyter Gmbh, 2015) Aydin, Neset; Diasamidze, Yasha; Sungur, Didem Yesil
    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.
  • [ X ]
    Öğe
    Some regular elements, idempotents and right units of complete semigroups of binary relations defined by semilattices of the class lower incomplete nets
    (Academic Press, 2014) Diasamidze, Yasha; Erdoğan, Ali; Aydin, Neşet
    In this paper, we investigate such a regular elements ? and idem-potents of the complete semigroup of binary relations BX(D) defined by semi-lattices of the class lower incomplete nets, for which V(D, ?) = Q. Also we investigate right units of the semigroup BX(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, idempotents and right units of the respective semigroup. © 2014 Academic Publications, Ltd.