Compact semigroups with square roots

Jane Maxwell Day

Vol. 36 (1971), No. 3, 623–630

DOI: 10.2140/pjm.1971.36.623

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