On Injective and Gorenstein Injective Dimensions of Local Cohomology Modules
2015 ◽
Vol 22
(spec01)
◽
pp. 935-946
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Keyword(s):
Let (R, 𝔪) be a commutative Noetherian local ring and M an R-module which is relative Cohen-Macaulay with respect to a proper ideal 𝔞 of R, and set n := ht M𝔞. We prove that injdim M < ∞ if and only if [Formula: see text] and that [Formula: see text]. We also prove that if R has a dualizing complex and Gid RM < ∞, then [Formula: see text]. Moreover if R and M are Cohen-Macaulay, then Gid RM < ∞ whenever [Formula: see text]. Next, for a finitely generated R-module M of dimension d, it is proved that if [Formula: see text] is Cohen-Macaulay and [Formula: see text], then [Formula: see text]. The above results have consequences which improve some known results and provide characterizations of Gorenstein rings.
2016 ◽
Vol 59
(2)
◽
pp. 403-416
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2019 ◽
Vol 18
(12)
◽
pp. 1950238
2016 ◽
Vol 15
(04)
◽
pp. 1650070
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2009 ◽
Vol 79
(1)
◽
pp. 59-67
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Keyword(s):
1981 ◽
Vol 24
(1)
◽
pp. 9-14
◽
1991 ◽
Vol 110
(3)
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pp. 421-429
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