Integral domains with highly nonunique factorization
For a positive integer \(n\), an atomic domain \(R\) is defined in the paper to be completely non-\(n\)-factorial if the product of any \(n\) atoms is divisible by the product of any \(n-1\) atoms. The authors prove that a domain \(R\) is completely non-\(n\)-factorial for some \(n\geq 2\) iff \(R\) is an atomic pseudo-valuation domain, equivalently, \((R,M)\) is quasilocal with \([M:M]\) a DVR with maximal ideal \(M\).
scientific article; zbMATH DE number 1140102