Prekrull整环的刻画

Some Characterizations of Prekrull Domains

讨论了Prekrull整环与几类主要整环之间的关系,证明了R是具有有限特征且满足局部主理想升链条件的Prekrull整环当且仅当R是Krull整环.给出整环R的每个扩环都是Prekrull整环且不是域,则R是广义Dedekind整环也是Pr櫣fer整环,以及在Prekrull整环上的多项式环的分式环仍是Prekrull整环的条件下,Prekrull整环的每个t linked扩环仍然是Prekrull整环,并证明了Prekrull整环在素v 理想局部化之后是离散赋值环.

In this paper, we study the relationship between Prekrull domains and several important domains. Especialy we prove that R is a Prekrull domain of finite character satisfying ascending chain conditions over principal ideals of R if and only if R is a Krull domain. And we have showed that each overring of R is a Prekrull domain, then R is a generalized Dedekind domain and Prüfer domain. Moreover, we characterize that each t-linked overring of a Prekrull domain is also a Prekrull domain if the quotient ring of the polynomial domain over a Prekrull domain is a Prekrull domain. Finally we indicate that the localization of a Prekrull domain at a prime v-ideal is a discrete valuation domain.