Unique factorization properties in commutative monoid rings with zero divisors
The authors defined and studied several different versions of ``factoriality'' for commutative rings with zero divisors. They provided necessary and sufficient conditions for a commutative monoid ring \(R[S]\) to be various kinds of ``unique factorization rings''. Their work generalizes Anderson et al.'s results about ``unique factorization'' in the polynomial ring \(R[X]\), Gilmer and Parker's characterization of factorial monoid domains, and Hardy and Shores's classification of when \(R[S]\) is a principal ideal ring (where \(S\) is a cancellative monoid). Also they studied when the monoid ring \(R[S]\) is ``restricted cancellative'' or satisfies various ``(restricted) ideal cancellation laws''.
unique factorization rings with zero divisors
scientific article; zbMATH DE number 7357025
scientific article