The eventual stability of depth, associated primes and cohomology of a graded module

Let R be a commutative Noetherian ring, M a finitely generated R-module, I an ideal of R and N a submodule of M such that IM ⫅ N. In this paper, the primary decomposition and irreducible decomposition of ideal I × N in the idealization of module R ⋉ M are given. From theses we get the formula for associated primes of R ⋉ M and the index of irreducibility of 0R ⋉ M.

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Associated primes and syzygies of linked modules

Journal of Commutative Algebra ◽

10.1216/jca-2019-11-3-301 ◽

2019 ◽

Vol 11 (3) ◽

pp. 301-323

Author(s):

Olgur Celikbas ◽

Mohammad T. Dibaei ◽

Mohsen Gheibi ◽

Arash Sadeghi ◽

Ryo Takahashi

Keyword(s):

Associated Primes

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On the associated graded module of an ideal generated by an unconditioned strong $d$-sequence

Journal of Mathematics of Kyoto University ◽

10.1215/kjm/1250517817 ◽

1999 ◽

Vol 39 (4) ◽

pp. 607-618 ◽

Cited By ~ 1

Author(s):

K. Khashyarmanesh ◽

SH. Salarian ◽

H. Zakeri

Keyword(s):

Graded Module

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Constructions of vector-valued modular forms of rank four and level one

International Journal of Number Theory ◽

10.1142/s1793042120500578 ◽

2020 ◽

Vol 16 (05) ◽

pp. 1111-1152

Author(s):

Cameron Franc ◽

Geoffrey Mason

Keyword(s):

Irreducible Representation ◽

Differential Equations ◽

Modular Forms ◽

Modular Group ◽

Tensor Products ◽

Two Dimensional ◽

Minimal Weight ◽

Graded Module ◽

Holomorphic Modular Forms ◽

Vector Valued

This paper studies modular forms of rank four and level one. There are two possibilities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we describe when each case occurs for general choices of exponents for the [Formula: see text]-matrix. In the remaining sections we describe how to write down the corresponding differential equations satisfied by minimal weight forms, and how to use these minimal weight forms to describe the entire graded module of holomorphic modular forms. Unfortunately, the differential equations that arise can only be solved recursively in general. We conclude the paper by studying the cases of tensor products of two-dimensional representations, symmetric cubes of two-dimensional representations, and inductions of two-dimensional representations of the subgroup of the modular group of index two. In these cases, the differential equations satisfied by minimal weight forms can be solved exactly.

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Local cohomology modules of a smooth $\mathbb{Z}$ -algebra have finitely many associated primes

Inventiones mathematicae ◽

10.1007/s00222-013-0490-z ◽

2013 ◽

Vol 197 (3) ◽

pp. 509-519 ◽

Cited By ~ 10

Author(s):

Bhargav Bhatt ◽

Manuel Blickle ◽

Gennady Lyubeznik ◽

Anurag K. Singh ◽

Wenliang Zhang

Keyword(s):

Local Cohomology ◽

Associated Primes ◽

Local Cohomology Modules ◽

Cohomology Modules

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The associated primes of local cohomology modules over rings of small dimension

manuscripta mathematica ◽

10.1007/s002290170024 ◽

2001 ◽

Vol 104 (4) ◽

pp. 519-525 ◽

Cited By ~ 45

Author(s):

Thomas Marley

Keyword(s):

Local Cohomology ◽

Small Dimension ◽

Associated Primes ◽

Local Cohomology Modules ◽

Cohomology Modules

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Chapter 16

The Diary of a Maritimer, 1816-1901 ◽

10.5949/liverpool/9780969588597.003.0016 ◽

1996 ◽

pp. 204-211

Keyword(s):

Eventual Stability

This final chapter documents Salter’s last move, to North Sydney, in 1878. It describes the eventual stability and success found by Salter in his late 70s as a ship’s broker and reports his death in 1901.

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