IJPAM: Volume 93, No. 4 (2014)

SOME REGULAR ELEMENTS, IDEMPOTENTS AND RIGHT
UNITS OF COMPLETE SEMIGROUPS OF BINARY
RELATIONS DEFINED BY SEMILATTICES OF
THE CLASS LOWER INCOMPLETE NETS

Yasha Diasamidze$^1$, Ali Erdogan$^2$, Neşet Aydın$^3$
$^1$Sh. Rustaveli State University
Batumi, GEORGIA
$^2$Department of Mathematics
Hacettepe University
Beytepe, Ankara, TURKEY
$^3$Department of Mathematics
Faculty of Arts and Sciences
Çanakkale Onsekiz Mart University
Çanakkale, TURKEY


Abstract. In this paper, we investigate such a regular elements $\alpha$ and idempotents of the complete semigroup of binary relations $B_{X}(D)$ defined by semilattices of the class lower incomplete nets, for which $V(D,\alpha)=Q$.

Also we investigate right units of the semigroup $B_{X}(Q)$. 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.

Received: January 30, 2014

AMS Subject Classification: 20M30, 20M10, 20M15

Key Words and Phrases: semigroups, binary relation, regular element, idempotents, right units

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DOI: 10.12732/ijpam.v93i4.6 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 4
Pages: 549 - 566

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).