On right unipotent semigroups
P. S. Venkatesan · Pacific Journal of Mathematics · 1976
We investigate the implications of certain conditions on right unipotent semigroups.We describe the greatest idempotent-separating congruence β on a right unipotent semigroup S. Necessary and sufficient conditions for (i) S to be a union of groups, (ii) S to be an inverse semigroup, (iii) the idempotents of S to be in the centre of S and (iv) the quotient semigroup S/β to be isomorphic with the subsemigroup of idempotents of S are also obtained.It is known that any regular semigroup has the greatest idempotent-separating congruence [5], [6] Such a congruence on an inverse semigroup was obtained by Howie [4].For the general terminology and notation the reader is referred to [1], [2].