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Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53904#.VNsFUyzQrzE Author(s)    Giuli Tavdgiridze , Yasha Diasamidze Affiliation(s) Department of Mathematics, Faculty of Physics, Mathematics and Computer Sciences, Shota Rustaveli Batumi State University, Batumi, Georgia . ABSTRACT In this paper we take subsemilattice of X -semilattice of unions D which satisfies the following conditions:                  We will investigate the properties of regular elements of the complete semigroup of binary relations B x ( D ) satisfying V ( D ,а)= 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 and right units of the respective semigroup.   KEYWORDS Semilattice , Semigroup , Regular Element , Right Unit , Binary Relation Cite this paper Tavdgiridze, G. and Diasami...

Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53795#.VNMhaCzQrzE Author(s)  Shota Makharadze 1 , Neşet Aydın 2 , Ali Erdoğan 3   Affiliation(s) 1 Shota Rustavelli University, Batum, Georgia . 2 &CCEDIL;anakkale Onsekiz Mart University, &CCEDIL;anakkale, Turkey . 3 Hacettepe University, Ankara, Turkey . ABSTRACT In this paper we give a full description of idempotent elements of the semigroup B X ( D ), which are defined by semilattices of the class <span "="">∑ 1 ( X , 10). For the case where X is a finite set we derive formulas by means of which we can calculate the numbers of idempotent elements of the respective semigroup.   KEYWORDS Semilattice , Semigroup , Binary Relation Cite this paper Makharadze, S. , Aydın, N. and Erdoğan, A. (2015) Complete Semigroups of Binary Relations Defined by Semilattices of the Class ∑ 1 ( X ,10). Applied Mathematics , 6 , 274-294. d...