Factorization in Integral Domains without Identity

Abstract

We investigate factorization in a nonzero integral domain A without identity. Now A may be viewed as a proper ideal of an integral domain D with identity having the same quotient field as A where \(A[1] \subseteq D \subseteq A:A\). We study the relationship between factorization in A and D, especially in the case where D = A[1] or A:A. Particular interest is given to various notions of unique factorization in A and to the relationship between A or D being atomic, satisfying ACCP, or being a bounded factorization domain, half-factorial domain, or finite factorization domain.