The construction D + XDS[X] and G-Prufer domains

초록

Let D be an integral domain with quotient field K, S a (not necessarily saturated) multiplicative subset of D and D + XDS[X] = {f ? D-S[X] | f (0) ? D}. In this paper, we show that D + XDS[X] is a G-Prufer domain if and only if D is a G- Prufer domain and D-S = K. We also prove that if D is a Bass domain (or a local NWF domain), then every finitely generated torsion-free module over D+XK[X] is isomorphic to a direct sum of some ideals.

키워드