Vol. 39, No. 3, 1971

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Uniquely representable semigroups. II

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

Vol. 39 (1971), No. 3, 573–579
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
Authors
J. T. Borrego
Haskell Cohen
Esmond Ernest Devun