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arXiv · 1607.04529

Relative Cohen-Macaulay filtered modules with a view toward relative Cohen-Macaulay modules

M. Mast Zohouri·Kh. Ahmadi Amoli·S. O. Faramarzi
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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.

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M. Mast Zohouri, Kh. Ahmadi Amoli, S. O. Faramarzi. 2016-07-15. Relative Cohen-Macaulay filtered modules with a view toward relative Cohen-Macaulay modules. https://arxiv.org/abs/1607.04529

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