Relative Cohen-Macaulay filtered modules with a view toward relative Cohen-Macaulay modules
Abstract
Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite R-module. It is shown that, if (R;m) is a complete local ring, then under certain conditions a contains a regular element on DR(Hc a(M)), where c = cd(a;M). A non-zerodivisor characterization of relative Cohen-Macaulay modules w.r.t a is given. We introduce the concept of relative Cohen-Macaulay filtered modules w.r.t a and study some basic properties of such modules. In paticular, we provide a non-zerodivisor characterization of relative Cohen-Macaulay filtered modules w.r.t a. Furthermore, a characterization of cohomological dimension filtration of M by the associated prime ideals of its factors is established. As a consequence, we present a cohomological dimension filtration for those modules whose zero submodule has a primary decomposition. Finally, we bring some new results about relative Cohen- Macaulay modules w.r.t a.
Cite
@article{arxiv.1607.04529,
title = {Relative Cohen-Macaulay filtered modules with a view toward relative Cohen-Macaulay modules},
author = {M. Mast Zohouri and Kh. Ahmadi Amoli and S. O. Faramarzi},
journal= {arXiv preprint arXiv:1607.04529},
year = {2017}
}
Comments
15 pages