On t-Dimension over Strong Mori Domains

In this note we prove that if R is a strong Mori domain with t-dim R = n and with countably many prime v-ideals, then there is a chain of rings between R and R^w R1=R belong to R2……belong to Rn lohtuin in R^w such that each R, is also a strong Mori domain and t-dim Rk=n - k ＋ 1 for k = 1,2,..., n.

强Prüfer环的同调刻画

设R是环,R的小finitistic维数定义为fPD(R)=sup{pd_(R)M|M∈FPR}.本文证明了:若R是连通的强Prüfer环,则fPD(R)≤1.也证明了若R是强Prufer环,M∈FPR,且M是Q-挠模,则pd_(R)M≤1.

A Note on the w-Global Transform of Mori Domains

Let R be a domain and let Rwg be the w-global transform of R. In this note it is shown that if R is a Mori domain, then the t-dimension formula t-dim（Rwg） = t-dim（R） - 1 holds.