Group rings and semigroup rings over Strong Mori domains

Abstract

In this paper we study the transfer of the property of being a Strong Mori domain. In particular we give the characterizations of Strong Mori domains in certain types of pullbacks. We show that if R is a Strong Mori domain which is not a field, then the polynomial ring R[{ X λ } λ∈ Λ ] is also a Strong Mori domain and w- dim R[{X λ} λ∈Λ]=w - dim R . We also determine necessary and sufficient conditions in order that the group ring R[ X; G] or the semigroup ring R[ X; S] should be a Strong Mori domain with w- dimension ≤1.