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Bounds for numbers of generators for a class of submodules of a finitely generated module

Tirdad Sharif·Siamak Yassemi
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Abstract

The aim of this paper is to obtain a uniform bound for a certain class of submodules from the following theorem: Let $(R,\frak m)$ be a local ring, let $M$ be a finite $R$--module of dimension $d\ge 1$ and let $\frak q$ be an ideal of $R$ generated by a system of parameters on $M$. Let $N$ be a submodule of $M$ with $\depth M/N\ge d-1$. Then $\ell(N/\frak qN)\le\ell(M/\frak qM)$.

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Tirdad Sharif, Siamak Yassemi. 2002-10-01. Bounds for numbers of generators for a class of submodules of a finitely generated module. https://arxiv.org/abs/math/0210002

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