منابع مشابه
On the ubiquity of Gorenstein rings
Introduction APIARY [23~, and subsequently GORENSTEIN Eg] and SAMUEL [2(r proved 9 3-~ t that if (2 is a point on a plane curve then no=2d Q, where dQ=dlmw0/ 9 Q and nQ = dim C'Q/~Q, 9 being the local ring of Q, CQ its normalization, and ~Q the conductor. This condition has received attention from a variety of algebraic geometers, and recently ROQUETTE [19J and BEI~GER [52 have put it i n a rat...
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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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In this paper, we extend the well-known Hilbert’s syzygy theorem to the Gorenstein homological dimensions of rings. Also, we study the Gorenstein homological dimensions of direct products of rings. Our results generate examples of non-Noetherian rings of finite Gorenstein dimensions and infinite classical weak dimension.
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 کاملPurity and Gorenstein Filtered Rings
In this paper, we discuss on the existence of filtrations of modules having good properties. In particular, we focus on filtered homomorphisms called strict, and show that there exists a filtration which makes a filtered homomorphism a strict filtered homomorphism. Moreover, by using this result, we study purity for filtered modules over a Gorenstein filtered ring.
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1969
ISSN: 2156-2261
DOI: 10.1215/kjm/1250523903