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arXiv · 2212.07122

Relative homological rings and modules

Parisa Pourghobadian·Kamran Divaani-Aazar·Ahad Rahimi
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Abstract

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.

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Parisa Pourghobadian, Kamran Divaani-Aazar, Ahad Rahimi. 2022-12-14. Relative homological rings and modules. https://arxiv.org/abs/2212.07122

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