Uniquely representable semigroups. II

J. T. Borrego, Haskell Cohen and Esmond Ernest Devun

Vol. 39 (1971), No. 3, 573–579

DOI: 10.2140/pjm.1971.39.573

Abstract

A semigroup S is said to be uniquely representable in terms of two subsets X and Yif X ⋅ Y = Y ⋅ X = S,x₁y₁,= x₂y₂ is a nonzero element of S implies x₁ = x₂ and y₁ = y₂ and y₁x₁ = y₂x₂ is a nonzero element of S implies y₁ = y₂ and x₁ = x₂ for all x₁,x₂ ∈ X and y₁,y₂ ∈ Y. In this paper we are concerned with semigroups S with no zero divisors, E(S) = {0,1}, and which are uniquely representable in terms of two subsets X and Y which are iseomorphic copies of the unusual unit interval. Here we show the nonzero elements of the semigroup S can be embedded in a Lie group.

Mathematical Subject Classification 2000

Primary: 22A15

Milestones

Received: 4 May 1970

Revised: 16 October 1970

Published: 1 December 1971