诱导算子与UMT整环(英文)

On Induced Operations and UMT-domains

设R T是整环扩张,定义了T上的由R的w 算子所诱导的星型算子wR,并给出了wR 乘法整环的特征.也讨论了环的w 整相关理论与环的w 整闭包,证明了在w 整扩张下,环R的w 维数与环T的wR 维数的一致性.还证明了一个整环R是UMT整环当且仅当R的w 整闭包Rw是wR 乘法整环.

Let RT be an extension of domains. In this paper we introduce the star-operation w_R of T induced by w-operation over R and obtain some characterizations of a w_R-multiplication domain. We discussion the w-integral dependence of an extension of rings and the w-integral closure of an extension of rings, and prove that R is a UMT-domain if and only if the w-integral closure R^w of R is a w_R-multiplication domain on the star-operation w of R^w induced by the w-operation of R.