منابع مشابه
Periodic modules over Gorenstein local rings
It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t ±1 ]-module associated to R. This module, denoted J(R), is the free Z[t ±1 ]-module on the isomorphism classes of finitely generated R-modules modulo relations reminiscent of those defining the Grothendieck group of R. The ...
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Let $(R, m)$ be a commutative noetherian local ring and let $Gamma$ be a finite group. It is proved that if $R$ admits a dualizing module, then the group ring $Rga$ has a dualizing bimodule as well. Moreover, it is shown that a finitely generated $Rga$-module $M$ has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an $R$-module.
متن کاملIntersection Multiplicities over Gorenstein Rings
LetR be a complete local ring of dimension d over a perfect field of prime characteristic p, and let M be an R-module of finite length and finite projective dimension. S. Dutta showed that the equality limn→∞ `(F n R(M)) pnd = `(M) holds when the ring R is a complete intersection or a Gorenstein ring of dimension at most 3. We construct a module over a Gorenstein ring R of dimension five for wh...
متن کاملGood Ideals in Gorenstein Local Rings
Let I be an m-primary ideal in a Gorenstein local ring (A,m) with dimA = d, and assume that I contains a parameter ideal Q in A as a reduction. We say that I is a good ideal in A if G = ∑ n≥0 I n/In+1 is a Gorenstein ring with a(G) = 1−d. The associated graded ring G of I is a Gorenstein ring with a(G) = −d if and only if I = Q. Hence good ideals in our sense are good ones next to the parameter...
متن کاملVanishing of Cohomology over Gorenstein Rings of Small Codimension
We prove that if M , N are finite modules over a Gorenstein local ring R of codimension at most 4, then the vanishing of Ext R (M,N) for n ≫ 0 is equivalent to the vanishing of Ext R (N,M) for n ≫ 0. Furthermore, if b R has no embedded deformation, then such vanishing occurs if and only if M or N has finite projective dimension.
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2018
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2018.12.2295