Group rings and semigroup rings over Strong Mori domains

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[{Xλ}λset membership, variantΛ] is also a Strong Mori domain and w-dim R[{Xλ}λset membership, variantΛ]=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.