Vol. 31, No. 2, 1969

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Factorizable semigroups

Kenneth Tolo

Vol. 31 (1969), No. 2, 523–535

A multiplicative semigroup S is said to be factorizable if it can be written as the set product AB of proper subsemigroups A and B. If this is possible, AB is called a factorization of S, with factors A and B. The factors are not required to be unique.

The following problems have been considered:

(I) Given a factorizable semigroup S = AB, where A and B are members of the semigroup classes P and Q, respectively (P and Q not necessarily distinct), to what semigroup class does S belong?

(II) What are sufficient conditions for the factorizability of a semigroup?

(III) Can the concept of factorizability be used in characterizing direct products of semigroups?

Mathematical Subject Classification
Primary: 20.93
Received: 6 November 1968
Published: 1 November 1969
Kenneth Tolo