Locally compact Clifford semigroups
James W. Stepp · Pacific Journal of Mathematics · 1970
Let S be a locally compact Hausdorff semigroup which is a disjoint union of subgroups one of which is dense.If S the disjoint union of exactly two groups one of which is compact, then S has been completely described by K. H. Hofmann, and if S is the disjoint union of two subgroups where the dense subgroup G has the added property that it is abelian and G/G o is a union of compact groups, then S has been described in a previous paper of the author.It is the purpose of this paper to consider S when each subgroup of S is a topological group when given the relative topology and G (the dense subgroup) has the added property that it is abelian and G/G o is a union of compact groups.In particular, we show how to reduce such a semigroup to a semigroup which is a union of real vector groups ( §3).In §4 we give the structure of S under the added assumption that E(S) is isomorphic to E[(R*) n ], where (12*)* denotes the n-folά product of the nonnegative real numbers under multiplication.2* Definitions and notations* If G is a topological group, G o