A characterization of uniquely divisible commutative semigroups

Dennison Robert Brown and J. G. LaTorre

Vol. 18 (1966), No. 1, 57–60

DOI: 10.2140/pjm.1966.18.57

Abstract

Let (S,+) be a commutative semigroup. If, for each x ∈ S, and for each positive integer n, there exists an (unique) element y of S such that x = ny, then S is (uniquely) divisible. In this note we present a more or less intrinsic characterization of uniquely divisible commutative semigroups and remark on a special sub-class of these semigroups in which it is possible to discern the fine structure of the addition.

Mathematical Subject Classification

Primary: 20.93

Milestones

Received: 18 February 1965

Published: 1 July 1966