Shahrood University of TechnologyJournal of Algebraic Systems2345-51286120180901THE LATTICE OF CONGRUENCES ON A TERNARY SEMIGROUP5970125510.22044/jas.2018.5360.1273ENN. AshrafiFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
Email: nashrafi@semnan.ac.irZ. YazdanmehrFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
Email: zhyazdanmehr@gmail.comJournal Article20170129In 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.http://jas.shahroodut.ac.ir/article_1255_585b8d0ca4e05982b434b1a9d2ab912e.pdf