CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Artinianness of Composed Graded Local Cohomology Modules

  Published:2016-02-11
 Printed: Jun 2016
  • Fatemeh Dehghani-Zadeh,
    Department of Mathematics, Yazd Branch, Islamic Azad university, Yazd, Iran
Format:   LaTeX   MathJax   PDF  

Abstract

Let $R=\bigoplus_{n\geq0}R_{n}$ be a graded Noetherian ring with local base ring $(R_{0}, \mathfrak{m}_{0})$ and let $R_{+}=\bigoplus_{n\gt 0}R_{n}$, $M$ and $N$ be finitely generated graded $R$-modules and $\mathfrak{a}=\mathfrak{a}_{0}+R_{+}$ an ideal of $R$. We show that $H^{j}_{\mathfrak{b}_{0}}(H^{i}_{\mathfrak{a}}(M,N))$ and $H^{i}_{\mathfrak{a}}(M, N)/\mathfrak{b}_{0}H^{i}_{\mathfrak{a}}(M,N)$ are Artinian for some $i^{,}s$ and $j^{,}s$ with a specified property, where $\mathfrak{b}_{o}$ is an ideal of $R_{0}$ such that $\mathfrak{a}_{0}+\mathfrak{b}_{0}$ is an $\mathfrak{m}_{0}$-primary ideal.
Keywords: generalized local cohomology, Artinian, graded module generalized local cohomology, Artinian, graded module
MSC Classifications: 13D45, 13E10, 16W50 show english descriptions Local cohomology [See also 14B15]
Artinian rings and modules, finite-dimensional algebras
Graded rings and modules
13D45 - Local cohomology [See also 14B15]
13E10 - Artinian rings and modules, finite-dimensional algebras
16W50 - Graded rings and modules
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/