Vol. 31, No. 2, 1969

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Semigroups satisfying identity xy = f(x, y)

Takayuki Tamura

Vol. 31 (1969), No. 2, 513–521
Abstract

Let f(x,y) be a word of length greater than 2 starting in y and ending in x. The purpose of this paper is to prove that a semigroup satisfies an identity xy = f(x,y) if and only if it is an inflation of a semilattice of groups satisfying the same identity. As its consequence we find a necessary and sufficient condition for xy = f(x,y) to imply commutativity.

Mathematical Subject Classification
Primary: 20.93
Milestones
Received: 25 May 1968
Published: 1 November 1969
Authors
Takayuki Tamura