Vol. 22, No. 1, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
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