Some regular elements, idempotents and right units of complete semigroups of binary relations defined by semilattices of the class lower incomplete nets

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.