ℋ-commutative semigroups in which each homomorphism is uniquely determined by its kernel

Edward Joseph Tully, Jr.

Vol. 45 (1973), No. 2, 669–679

DOI: 10.2140/pjm.1973.45.669

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