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arXiv · 2009.10407

The $\mathfrak{a}$-Filter grade of an ideal $\mathfrak{b}$ and $(\mathfrak{a},\mathfrak{b})$-$\mathrm{f}$-modules

Jingwen Shen·Xiaoyan Yang
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Abstract

Let $\mathfrak{a},\mathfrak{b}$ be two ideals of a commutative noetherian ring $R$ and $M$ a finitely generated $R$-module.~We continue to study $\textrm{f}\textrm{-}\mathrm{grad}_R(\mathfrak{a},\mathfrak{b},M)$ which was introduced in [Bull. Malays. Math. Sci. Soc. 38 (2015) 467--482], some computations and bounds of $\textrm{f}\textrm{-}\mathrm{grad}_R(\mathfrak{a},\mathfrak{b},M)$ are provided.~We also give the structure of $(\mathfrak{a},\mathfrak{b})$-$\mathrm{f}$-modules,~various properties which are analogous to those of Cohen Macaulay modules are discovered.

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Jingwen Shen, Xiaoyan Yang. 2020-09-22. The $\mathfrak{a}$-Filter grade of an ideal $\mathfrak{b}$ and $(\mathfrak{a},\mathfrak{b})$-$\mathrm{f}$-modules. https://arxiv.org/abs/2009.10407

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