THE LATTICE OF CONGRUENCES ON A TERNARY SEMIGROUP

Document Type : Original Manuscript

Authors

1 Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: nashrafi@semnan.ac.ir

2 Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: zhyazdanmehr@gmail.com

Abstract

In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular, it is not even semimodular. Then we indicate some conditions under which this lattice is modular.

Keywords

Journal of Algebraic Systems
Volume 6, Issue 1
September 2018
Pages 59-70

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