(t,v)-Dedekind整环的局部化问题

Localizations of(t,v)-Dedekind Domains

证明了整环R是(*,v)-Dedekind整环当且仅当R[X]N*是拟Dedekind整环当且仅当R[X]N*是拟主理想整环.特别地,取星型算子*=v时,证明了整环R是(t,v)-Dedekind整环当且仅当R[X]Nv是拟Dedekind整环当且仅当R[X]Nv是拟主理想整环.同时,举例说明了(t,v)-Dedekind整环与弱分解整环之间的关系,并给出了当整环R是弱分解整环时,R是(t,v)-Dedekind整环当且仅当R是拟Dedekind整环当且仅当R是拟主理想整环.

In this paper,we show that R is a(*,v)-Dedekind domain if and only if R[X]N* is a pseudo-Dedekind domain if and only if R[X]N* is pseudo-principal.Especially,we indicate that R is a(t,v)-Dedekind domain if and only if R[X]Nv is a pseudo-Dedekind domain if and only if R[X]Nv is pseudo-principal.Also,we give an example,which indicates the connection between a weakly factorial domain and a(t,v)-Dedekind domain.We show that if R is a weakly factorial domain,then R is a(t,v)-Dedekind domain if and only if R is a pseudo-Dedekind domain and if and only if R is pseudo-principal.