Commutative semigroups which are almost finite

Bruce Ansgar Jensen and Donald Wright Miller

Vol. 27 (1968), No. 3, 533–538

DOI: 10.2140/pjm.1968.27.533

Abstract

Semigroups satisfying certain finiteness conditions are studied. It is shown that an infinite semigroup S every proper subsemigroup of which is finite is a group; thus in particular if S is commutative then it is isomorphic to the group Z(p^∞) for some prime p. An infinite commutative semigroup every proper homomorph of which is finite is shown to be imbeddable in an infinite cyclic group with zero element adjoined and its structure is described.

Mathematical Subject Classification

Primary: 20.93

Milestones

Received: 31 October 1967

Published: 1 December 1968