摘要:Let R(*)T be an extension of domains. In this paper we introduce the star-operation wR of T induced by w-operation over R and obtain some characterizations of a wR-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 Rw of R is a wR-multiplication domain on the star-operation w of Rw induced by the w-operation of R.%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.