Cancellation law and unique factorization theorem for string operations
In this paper, we extend Hoit's results by replacing the Abelian group (Zm') by an arbitrary monoid (A, o). The set of strings built up from the alphabet A is denoted by String(A). We extend the operation ◦ on the alphabet set A to the string set String(A). We show that (String(A), o) is a monoid if and only if (A, ◦) is a monoid. When (A,o) is a group, we prove that stronger versions of a cancellation law and unique factorization hold for (String(A), o). A general criterion for two irreducible strings to commute is also presented.