Factorization in integral domains without identity
The aim of this paper is to study factorization in a nonzero commutative integral domain \(A\) without identity. Considering \(A\) as a proper ideal of an integral domain \(D\) with identity having the same quotient field \(K\) as \(A\), with \(A[1]\subseteq D \subseteq A:A\), where \(1\) is the identity element of \(K\) and \(A:A = \{\,x\in K\,|\,xA \subseteq A\,\}\), the author investigates the relationship between factorization in \(A\) and \(D\), mainly when \(D=A[1]\) or \(D= A:A\). Thus, various generalizations of unique factorization are studied in \(A\), as well as the relationship between the property of \(A\) or \(D\) being atomic, or a bounded factorization domain, or a half-factorial domain, or a finite factorization domain, or satisfying the ACC on principal ideals, etc.
scientific article; zbMATH DE number 5659727