Factorizations and Monoids

Abstract

In this paper we introduce the notion of generalized factorization for an arbitrary submonoid M subset of A*, where A* is the free monoid generated by an alphabet A, generalizing, in this way, the notion of factorization of A*. Then we give a characterization of the free product of two submonoids of A* in terms of unambiguous products of monoids. To do this we make use of the notion of coding partition of a set X subset of A(+), where A+ is the free semigroup generated by an alphabet A. Moreover, given a coding partition of a set X subset of A(+), we will show how to construct a generalized factorization of X *.