关于PVMD的一些刻画

证明了R是PVMD当且仅当每个无挠R-模是w-平坦模,当且仅当每个有限生成无挠R-模是w-投射模.讨论了PVMD的环扩张与PVMD中的素w-理想的性质.特别地,对于PVMD中的素w-理想p,给出了其是分支的一些等价刻画,得到p是分支的当且仅当存在一个w-理想I≠p,使得p=I,当且仅当p是一个主理想上的极小素理想.     

PTW整环的刻画

引入了PTW整环的概念，刻画了PTW整环的局部化性质，然后对PTW整环的拉回图进行了研究，证明了若RDTF是强Milnor方图，则w-dim（R）=max{htτM＋w-dim（D），w-dim（T）}，最后通过例子说明了PTW整环不是TW整环．     

A Note on the w-Global Transform of Mori Domains

Let R be a domain and let R wg 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(R wg ) = t- dim(R) - 1 holds.     

关于Mori整环的$w$-全局变换环的注记

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.     

Integral Domains in Which Each Ideal Is a W-Ideal

ABSTRACT

In this paper, we investigate integral domains in which each ideal is a w-ideal (i.e. the d- and w-operations are the same), called the DW-domains. In some sense this study is similar to that one given in Houston and Zafrullah (1988 Houston , E. , Zafrullah , M. (1988). Integral domains in which each t-ideal is divisorial. Michigan Math. J. 35:291–300. [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) [Houston, E., Zafrullah, M. (1988). Integral domains in which each t-ideal is divisorial. Michigan Math. J. 35:291–300.] for the TV-domains. We prove that a domain R is a DW-domain if and only if each maximal ideal of R is a w-ideal, and if R is a domain such that R _M is a DW-ideal for each maximal ideal M of R, then so is R, and the equivalence holds when R is v-coherent. We describe the w-operation on pull–backs in order to provide original examples.

     

诱导算子与UMT整环

设R包含于T是整环扩张，定义了T上的由R的ω-算子所诱导的星型算子ωR，并给出了ωR-乘法整环的特征．也讨论了环的ω-整相关理论与环的ω-整闭包，证明了在ω-整扩张下，环R的ω-维数与环T的ωR-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ω-整闭包R^ω是ωR-乘法整环．