International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 12, Pages 849-854
doi:10.1155/S0161171200003604

Right simple subsemigroups and right subgroups of compact convergence semigroups

Abstract

Clifford and Preston (1961) showed several important characterizations of right groups. It was shown in Roy and So (1998) that, among topological semigroups, compact right simple or left cancellative semigroups are in fact right groups, and the closure of a right simple subsemigroup of a compact semigroup is always a right subgroup. In this paper, it is shown that such results can be generalized in convergence semigroups. In the discussion of maximal right simple subsemigroups and maximal right subgroups of semigroups, generalization of the results that no two maximal right simple subsemigroups and maximal right subgroups of a convergence semigroup intersect, is also established.