Vol. 45, No. 2, 1973

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ISSN: 0030-8730
-commutative semigroups in which each homomorphism is uniquely determined by its kernel

Edward Joseph Tully, Jr.

Vol. 45 (1973), No. 2, 669–679
Abstract

An eqivalence relation σ on a semigroup S is called a congruence if whenever aσb and cσd it follows that acσbd. There is a natural correspondence between congruences on S and homomorphic images of S. In this paper semigroups satisfying the following two conditions are considered.

(1) There exists g in S such that, if σ and ρ are congruences on S and {x S;xσg} = {x S : xρg}, then σ and ρ coincide.

(2) For all a,b lS, either ab = ba or, for some x and y in S,abx = ba and yab = ba.

Mathematical Subject Classification 2000
Primary: 20M10
Milestones
Received: 6 January 1967
Revised: 21 December 1972
Published: 1 April 1973
Authors
Edward Joseph Tully, Jr.