Semigroups satisfying identity xy = f(x, y)

Takayuki Tamura

Vol. 31 (1969), No. 2, 513–521

DOI: 10.2140/pjm.1969.31.513

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