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Relative Cohen-Macaulay filtered modules with a view toward relative Cohen-Macaulay modules | | M. Mast Zohouri
; Kh. Ahmadi Amoli
; S.O. Faramarzi
; | | Date: |
15 Jul 2016 | | Abstract: | Let $R$ be a commutative Noetherian ring and $M$ be a finite $R$-module. We
introduce and study the concept of relative Cohen-Macaulay filtered modules
with respect to a proper ideal $I$ of $R$. For a complete local ring
$(R,mathfrak{m})$, we show that $I$ contains a regular element on
$D_{R}(H^{c}_{I}(M))$, where $c=operatorname{cd}(I,M)$ and as its application,
a non-zerodivisor characterization of relative Cohen-Macaulay modules is given.
Furthermore, a characterization of cohomological dimension filtration of $M$ by
the associated prime ideals of its factors is given. As a corollary of this
characterization, we present a cohomological dimension filtration for certain
modules. Also, we provide some results about relative Cohen-Macaulay modules. | | Source: | arXiv, 1607.4529 | | Services: | Forum | Review | PDF | Favorites | |
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