Document Type: Original Manuscript
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: email@example.com
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: firstname.lastname@example.org
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.