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