2014
DOI: 10.1142/s0219498815500425
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On the relative Cohen–Macaulay modules

Abstract: Let R be a commutative Noetherian local ring and let a be a proper ideal of R. In this paper, as a main result, it is shown that if M is a Gorenstein R-module with c = ht M a, then H i a (M ) = 0 for all i = c is completely encoded in homological properties of H c a (M ), in particular in its Bass numbers. Notice that, this result provides a generalization of a result of Hellus and Schenzel which has been proved before, as a main result, in the case where M = R.

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Cited by 6 publications
(3 citation statements)
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“…Several authors followed up on relative Cohen-Macaulay modules; see e.g. [HSt,Sc2,R,JR,Ra2,RZ1,CH,Ra1,DGTZ1,Sc1,DGTZ2]. In particular, in [DGTZ2] the authors introduce the notion of arelative system of parameters which appears to be quite useful in studying relative Cohen-Macaulay modules.…”
Section: Introductionmentioning
confidence: 99%
“…Several authors followed up on relative Cohen-Macaulay modules; see e.g. [HSt,Sc2,R,JR,Ra2,RZ1,CH,Ra1,DGTZ1,Sc1,DGTZ2]. In particular, in [DGTZ2] the authors introduce the notion of arelative system of parameters which appears to be quite useful in studying relative Cohen-Macaulay modules.…”
Section: Introductionmentioning
confidence: 99%
“…In recent years, many authors have studied cohomologically complete intersection ideals for M ¼ R. The first attempt in this direction was made by M. Hellus and P. Schenzel in [8, Theorem 0.1]. Later on, M. Zargar provided with some conditions for a maximal Cohen-Macaulay module of finite injective dimension to be a cohomologically complete intersection (see [27,Theorem 1.1]). The similar results are obtained for the canonical modules in [15,Theorem 1.1].…”
Section: Introductionmentioning
confidence: 99%
“…A characterization of ideals such that H i I (R) = 0 for all i = g, so-called cohomologically complete intersections, is described by Hellus and the author (see [13]). Some of these results were generalized to finitely generated modules by Zargar (see [26]) under the name relative Cohen-Macaulay modules. In the case of a Gorenstein ring (R, m) weaker conditions than H i I (R) = 0 for i = grade(I, R) are sufficient for the previous isomorphisms (see [24]).…”
Section: Introductionmentioning
confidence: 99%