Vol. 36, No. 3, 1971

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Compact semigroups with square roots

Jane Maxwell Day

Vol. 36 (1971), No. 3, 623–630
Abstract

Suppose that S is a finite dimensional cancellative commutative clan with E = {0,1} and that H is the group of units of S. We show that if square roots exist in S∕H, not necessarily uniquely, then there is a closed positive cone T in En for some n and a homomorphism f : (T ∪∞) × H S which is onto and one-to-one on some neighborhood of the identity. T ∪∞ denotes the one point compactification of T.

Mathematical Subject Classification 2000
Primary: 22A15
Milestones
Received: 2 August 1969
Revised: 23 June 1970
Published: 1 March 1971
Authors
Jane Maxwell Day