# On a new invariant of finitely generated modules over local rings

@article{Cuong2010OnAN,
title={On a new invariant of finitely generated modules over local rings},
author={Nguyen Tu Cuong and Doan Trung Cuong and Hoang Le Truong},
journal={arXiv: Commutative Algebra},
year={2010}
}
• Published 21 March 2010
• Mathematics
• arXiv: Commutative Algebra
Let $M$ be a finitely generated module on a local ring $R$ and $\F: M_0\subset M_1\subset...\subset M_t=M$ a filtration of submodules of $M$ such that $d_o<d_1< ... <d_t=d$, where $d_i=\dim M_i$. This paper is concerned with a non-negative integer $p_\mathcal F(M)$ which is defined as the least degree of all polynomials in $n_1, ..., n_d$ bounding above the function $$\ell(M/(x_1^{n_1}, ..., x_d^{n_d})M)-\sum_{i=0}^tn_1...n_{d_i}e(x_1,..., x_{d_i};M_i).$$ We prove that $p_\mathcal F(M)$ is…
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