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?
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