Cancellation law and unique factorization theorem for string operations

Authors

Joseph Tonien, University of WollongongFollow

RIS ID

101567

Publication Details

Tonien, D. (2006). Cancellation law and unique factorization theorem for string operations. Journal of Algebra and its Applications, 5 (2), 231-243.

Abstract

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.