Quasilength, latent regular sequences, and content of local cohomology

Quasilength, Latent Regular Sequences, and Content of Local Cohomology

We use the notion of quasilength to introduce a nonnegative real number hx(M) that is intended heuristically as a “measure” of the local cohomology module H I (M). It is defined as a limit or lim inf of normalized quasilengths: see §2. When x is understood from context we shall also refer to this real number as the h-content of M . The positivity of hx(R) gives a necessary condition for there t...

On Reducing sequences and an Application to Local Cohomology Modules

on reducing sequences and an application to local cohomology modules

Note on regular and coregular sequences

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

TOP LOCAL COHOMOLOGY AND TOP FORMAL LOCAL COHOMOLOGY MODULES WITH SPECIFIED ATTACHED PRIMES

Let (R,m) be a Noetherian local ring, M be a finitely generated R-module of dimension n and a be an ideal of R. In this paper, generalizing the main results of Dibaei and Jafari [3] and Rezaei [8], we will show that if T is a subset of AsshR M, then there exists an ideal a of R such that AttR Hna (M)=T. As an application, we give some relationships between top local cohomology modules and top f...