On the CD-filtration of modules with respect to a system of ideals

Document Type : Research Paper

Authors

1 Department of mathematics, Science faculty, Payeme Noor University, Tehran, Iran

2 Department of Mathematics, Payame Noor University, Tehran. Iran

Abstract

In this paper, we introduce the concept of the cohomological dimension filtration with respect to a system of ideals.
In particular, a characterization of cohomological dimension filtration of a module by the associated prime ideals of its factors is established. As a main result, we provide a necessary and sufficient condition for an ascending chain of submodules of an $\mathfrak{R}$ -module $M$ to be the $\mathrm{cd}$-filtration of $M$, with respect to a system of ideals.
 
 

Keywords


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