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… 
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References

SHOWING 1-10 OF 11 REFERENCES
ON THE DIMENSION FILTRATION AND COHEN-MACAULAY FILTERED MODULES
For a finitely generated A-module M we define the dimension filtrationM= {Mi}0≤i≤d, d = dimAM, whereMi denotes the largest submodule of M of dimension ≤ i. Several properties of this filtration are
On the least degree of polynomials bounding above the differences between lengths and multiplicities of certain systems of parameters in local rings
Let A be a commutative local Noetherian ring with the maximal ideal m and M a finitely generated A-module, d = dim M. It is well-known that the difference between the length and the multiplicity of a
Cohen-Macaulay rings
In this chapter we introduce the class of Cohen–Macaulay rings and two subclasses, the regular rings and the complete intersections. The definition of Cohen–Macaulay ring is sufficiently general to
Sequentially Cohen-Macaulay Modules Under Base Change
ABSTRACT Assume that ϕ:(R, ± 𝔪) → (S, ± 𝔫) is a local flat homomorphism between commutative Noetherian local rings R and S. Let M be a finitely generated R-module. We investigate the ascent and
On sequentially Cohen-Macaulay modules
In this paper we present characterizations of sequentially Cohen-Macaulay modules in terms of systems of parameters, which are generalizations of well-known results on Cohen-Macaulay and generalized
Combinatorics and commutative algebra
This text offers an overview of two of the main topics in the connections between commutative algebra and combinatorics. The first concerns the solutions of linear equations in non-negative integers.
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