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 ...
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 کاملOn Sums of Squares in Local Rings
Let A be a semilocal ring. We compare the set of positive semidefinite (psd) elements of A and the set of sums of squares in A. For psd f ∈ A, whether f is a sum of squares or not depends only on the behavior of f in an infinitesimal neighborhood of the real zeros of f in Spec A. We apply this observation, first to 1-dimensional local rings, then to 2-dimensional regular semilocal rings. For th...
متن کاملCohen-lenstra Sums over Local Rings
où R est un anneau commutatif local et u est un entier non-negatif, la sommation s’étendant sur tous les R-modules finis, à isomorphisme prés. Ce problème est motivé par les heuristiques de Cohen et Lenstra sur les groupes des classes des corps de nombres, où de telles sommes apparaissent. Si R a des propriétés additionelles, on reliera les sommes ci-dessus à une limite de fonctions zêta des mo...
متن کاملGorenstein rings through face rings of manifolds
The face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the sphere g-conjecture implies all enumerative consequences of its far reaching generalization (due to Kalai) to manifolds. A special case of Kalai’s manifold g-c...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2012
ISSN: 1435-5345,0075-4102
DOI: 10.1515/crelle.2011.132