IJPAM: Volume 86, No. 1 (2013)

REGULAR ELEMENTS OF THE COMPLETE SEMIGROUPS
OF BINARY RELATIONS OF THE CLASS \sum7(X,8)

Barış Albayrak1, I. Yasha Diasamidze2, Neşet Aydin3
1,3Department of Mathematics
Faculty of Science and Art
Canakkale Onsekiz Mart University
Canakkale, TURKEY
2Shota Rustaveli State University
35, Ninoshvili St., Batumi 6010, GEORGIA


Abstract. In this paper let Q={T1,T2,T3,T4,T5,T6,T7,T8} be a subsemilattice of:
T1 ⊂ T2 ⊂ T3 ⊂ T5 ⊂ T6 ⊂ T8,
T1 ⊂ T2 ⊂ T3 ⊂ T5 ⊂ T7 ⊂ T8,
T1 ⊂ T2 ⊂ T4 ⊂ T5 ⊂ T6 ⊂ T8,
T1 ⊂ T2 ⊂ T4 ⊂ T5 ⊂ T7 ⊂ T8,
T1 ⊂ T2 ⊂ T4 ⊂ T5 ⊂ T7 ⊂ T8,
T4 \ T3 ≠ ∅,
T3 \ T4 ≠ ∅,
T6 \ T7 ≠ ∅,
T7 \ T6 ≠ ∅,
T3 ∪ T4=T5,
T6 ∪ T7=T8,
T6 ∪ T7=T8,
then we characterize the class each element of which is isomorphic to Q by means of the characteristic family of sets, the characteristic mapping and the generate set of Q. Moreover, we calculate the number of regular elements of BX(D) for a finite set X.

Received: May 8, 2013

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

Key Words and Phrases: semigroups, binary relation, regular elements

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DOI: 10.12732/ijpam.v86i1.13 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: 2013
Volume: 86
Issue: 1