UMT整环上的w-维数

w-Dimension of UMT-Domains

设R是整环,X是R上的一个未定元,{Xλ}λ∈Λ是R上任意多个未定元的集合.证明了若R是UMT整环,则w-dimR=w-dim(R[{Xλ}λ∈Λ]).进一步研究了UMT整环上的群环,证明了若R是UMT整环,则w-dimR=w-dimR[X;G].

Let R be an integral domain and X an indeterminate （respectively,{Xλ}λ∈Λ a set of arbitrary indeterminates） over R.In this paper, we show that if R is a UMT-domain, then w-dim R =w-dim（R[{Xλ}λ∈Λ]）.We further characterize the group ring R[X;G]over a UMT-domain R and prove that w-dim R=w-dimR[X;G].