论文标题
相对同源环和模块
Relative homological rings and modules
论文作者
论文摘要
具有同源标准的环和模块的研究是交换代数的基石。让$ r $成为具有身份（不一定是本地）和$ \ $ $ r $的$ \ frak a $的noetherian戒指。在本文中，开发了同源环和模块理论的相对类似物。我们介绍了$ \ frak的概念，$ relative的常规，$ \ frak a $ relativate a-relative totalstection和$ \ frak a $ relative gorenstein rings and Modules。我们通过证明这些类型的环和模块之间的一些相互作用来扩展一些经典结果。
The study of rings and modules with homological criteria is a cornerstone of commutative algebra. Let $R$ be a commutative Noetherian ring with identity (not necessarily local) and $\frak a$ a proper ideal of $R$. In this paper, a relative analogue of the theory of homological rings and modules is developed. We introduce the notions of $\frak a$-relative regular, $\frak a$-relative complete intersection, and $\frak a$-relative Gorenstein rings and modules. We extend some classical results by demonstrating some interactions between these types of rings and modules.
