On a general theory of factorization in integral domains

Abstract

This paper introduces a general theory of factorization of elements in integral domains. This theory subsumes most if not all previously studied cases such as the usual factorization into irreducible elements or into prime elements; the factorization into distinguished classes of elements such as prime powers, primary, or t-pure elements, and the comaximal factorizations of McAdam and Swan. © 2011 Rocky Mountain Mathematics Consortium.