Vol. 22, No. 1, 1967

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A semigroup union of disjoint locally finite subsemigroups which is not locally finite

Thomas Craig Brown

Vol. 22 (1967), No. 1, 11–14
Abstract

The semigroup S of the title is the free semigroup F on four generators factored by the congruence generated by the set of relations {w2 = w3|w F}. The following lemma is proved by examining the elements of a given congruence class of F:

Lemma. If x,y S and x2 = y2, then either xy = x2 or yx = x2.

From the Lemma it then easily follows that the (disjoint) subsemigroups {y S|y2 = x2} of S are locally finite.

Mathematical Subject Classification
Primary: 20.18
Milestones
Received: 19 December 1966
Published: 1 July 1967
Authors
Thomas Craig Brown