# 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} }

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…

## 4 Citations

Some loci related to Cohen–Macaulayness

- Mathematics
- 2014

Let (R, 𝔪) be a Noetherian local ring and M a finitely generated R-module. The pseudo Cohen–Macaulayness (respectively, generalized Cohen–Macaulayness) was introduced by Cuong–Nhan [Pseudo…

Non-Cohen-Macaulay Locus and Non Generalized Cohen-Macaulay Locus

- Mathematics
- 2014

Let (R, 𝔪) be a Noetherian local ring and M a finitely generated R-module. In this paper, we improve and extend some known relations among the non-Cohen–Macaulay locus nCM(M), the polynomial type…

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