Abstract

We introduce and study the notion of ES-w-stability for an integral domain R. A nonzero ideal I of R is called ES-w-stable if ${(I^2)}_w={(JI)}_w$ for some t-invertible ideal J of R contained in I, and I is called weakly ES-w-stable if $I_w={(JE)}_w$ for some t-invertible fractional ideal J of R and w-idempotent fractional ideal E of R. We define R to be an ES-w-stable domain (resp., a weakly ES-w-stable domain) if every nonzero ideal of R is ES-w-stable (resp., weakly ES-w-stable). These notions allow us to generalize some well-known properties of ES-stable and weakly ES-stable domains.

摘要

我们介绍并研究了积分域R的 ES- w稳定性的概念。非零理想我的- [R被称为ES-W-稳定如果${({\mathrm{一世}}^2)}_{瓦}={(J\mathrm{一世})}_{瓦}$对于一些吨-invertible理想Ĵ的ř包含在我和我被称为弱ES-W-稳定如果${\mathrm{一世}}_{瓦}={(J乙)}_{瓦}$对于一些吨-invertible分式理想Ĵ的ř和瓦特-idempotent分式理想Ë的ř。我们定义- [R是一个ES-W-稳定域（分别，一个弱ES-W-稳定域）如果每个非零理想ř是ES-瓦特-stable（相应的，弱ES-瓦特-stable）。这些概念使我们能够概括一些众所周知的 ES 稳定域和弱 ES 稳定域的特性。