Vol. 35, No. 3, 1970

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Notes on commutative power joined semigroups

Richard G. Levin and Takayuki Tamura

Vol. 35 (1970), No. 3, 673–679
Abstract

Let S be a commutative semigroup. The main theorem in this paper is to prove that the following two conditions are equivalent: (1) For all a,b S there are positive integers m,n such that am = bn. (2) For all a,b S,al = ambn,bγ = bsat for some l,m,n,r,s,t. As a consequence of the theorem, the authors prove that a commutative archimedean semigroup S without idempotent is power joined if and only if the structure group of S is a torsion group.

Mathematical Subject Classification
Primary: 20.93
Milestones
Received: 9 October 1969
Revised: 9 June 1970
Published: 1 December 1970
Authors
Richard G. Levin
Takayuki Tamura