Vol. 27, No. 3, 1968

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ISSN: 0030-8730
Commutative semigroups which are almost finite

Bruce Ansgar Jensen and Donald Wright Miller

Vol. 27 (1968), No. 3, 533–538

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
Received: 31 October 1967
Published: 1 December 1968
Bruce Ansgar Jensen
Donald Wright Miller