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Showing 1 to 20 of 26 for “"Gorenstein"”.
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On Gorenstein Projective and Gorenstein Flat Modules
… homological algebra has a counterpart in Gorenstein homological algebra". We support this statement by showing over commutative Noetherian rings of finite Krull dimension, every Gorenstein at module has finite Gorenstein projective dimension. This statement is the Gorenstein counterpart of …
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Gorenstein Injective Modules
One of the open problems in Gorenstein homological algebra is: when is the class of Gorenstein injective modules closed under arbitrary direct sums? Our main result gives a sufficient condition for this to happen. We prove that when the ring R is noetherian and such that every R-module has finite …
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Trivial Extensions and Gorenstein Rings
Made available in DSpace on 2015-05-12T22:37:39Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 7212352.PDF: 1792518 bytes, checksum: d2c27142acc08a9f6eae81a8c4381be2 (MD5) Previous issue date: 1971
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Weak Purity for Gorenstein Rings
… this setting, etale). When the ring B is merely Gorenstein, there are numerous examples which show that A need not be Cohen-Macaulay, hence that the extension need not be unramified. In a related context, the main portion of the thesis addresses the purity of the extension $B\to A.$ The setting …
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Hochschild Cohomology of Short Gorenstein Rings
… the Hochschild cohomology of the family of short Gorenstein k-algebras </p><p>sGor(N) =k[X_0,...,X_N](X_iX_j, X_i^2−X_j^2 | i,j= 0,...,N, i different from j), N≥2,</p><p>exhibits exponential growth. The proof uses Gröbner-Shirshov basis theory and along the way we describe an explicit monomial …
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Hochschild Cohomology Of Short Gorenstein Rings
… the Hochschild cohomology of the family of short Gorenstein k-algebras </p><p>sGor(N) =k[X_0,...,X_N](X_iX_j, X_i^2−X_j^2 | i,j= 0,...,N, i different from j), N≥2,</p><p>exhibits exponential growth. The proof uses Gröbner-Shirshov basis theory and along the way we describe an explicit monomial …
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On Gorenstein Rings and G-Dimension
<p>Gorenstein rings are presented and characterized, and the concept of Gorenstein dimension, which parallels projective dimension for modules and rings, is introduced.</p>
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Auslander-Reiten Sequences over Gorenstein Rings of Dimension One
<p>Let R be a complete local Gorenstein ring of dimension one, with maximal ideal m. We show that if M is a maximal Cohen-Macaulay R-module which begins an Auslander-Reiten sequence, then this sequence is produced by an endomorphism of m, which we call a Frobenius element. We observe that Frobenius …
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Local enumerative invariants of some Gorenstein surfaces and orbifolds
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms
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On Descent in Dimension Two and Non-Split Gorenstein Modules (Algebra, Commutative)
We show that the question of the decomposition of Gorenstein modules over normal domains can be reduced to the same question over normal domains of low dimension (that is, dimension four or less).
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Shannon extensions of regular local rings. Lefschetz properties for Gorenstein graded algebras associated to Apery Sets.
… per due classi di algebre graduate Artiniane di Gorenstein associate in modo naturale agli Apery set di semigruppi numerici. A questo scopo, viene provato un risultato generale sul trasferimento della proprietà di Lefschetz debole da un'algebra Artiniana Gorenstein ad un suo quoziente modulo un …
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Complete Mirror Pairs and Their Naive Stringy Hodge Numbers
… dotsc,\Delta_c},Y_{\nabla_1,\dotsc,\nabla_c})$ in Gorenstein Fano</p><p>toric varieties $(X_\Delta,X_\nabla)$. These Calabi-Yau varieties are singular</p><p>in general. Batyrev and Nill have developed a generating function $\Est$ for the</p><p>stringy Hodge numbers of Batyrev-Borisov mirror pairs. …
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Representation Theory of Orders over Cohen-Macaulay Rings
… idea was introduced by Van den Bergh [45] for R Gorenstein and we</p> <p>investigate the generalization to the case where R is Cohen-Macaulay. We show that if</p> <p>an order is totally reflexive over R and has finite global dimension, then R was already</p> <p>Gorenstein. Further, we investigate …
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The topology of terminal quartic 3-folds
… divisors. More generally, let Y be a terminal Gorenstein Fano 3-fold with Picard rank 1. Denote by s(Y )=h_4 (Y )-h^2 (Y ) = h_4 (Y )-1 the defect of Y. A variety is Q-factorial when every Weil divisor is Q-Cartier. The defect of Y is non-zero precisely when the Fano 3-fold Y is not …
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Generalized Koszul Properties of Commutative Local Rings
… we prove that the Ext algebra of a compressed Gorenstein local ring of even socle degree is generated in degrees 1 and 2.
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Surfaces Isogenous to a Product: Their Automorphisms and Degenerations
… on them. As a result, I show that the Q-Gorenstein deformations of the degenerations with certain singuarities are unobstructed and get some connected components of the moduli space of stable surfaces.
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Some special cases of Chow groups of complete ramified regular local rings
… dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, (I) = 0 in $A\sb{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, (P) = 0 in $A\sb{n-i}(R).$ We also study the above problem when the Eisenstein polynomial is of the form $f = p …
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Components of the Emerton-Gee Moduli Stack of Galois Representations for GL2 and A Graph-Theoretic Approach to Computing Selmer Groups of Elliptic Curves over Q(i)
… are smooth, which are normal, and which have Gorenstein normalizations. We prove that the normalizations of these components admit smooth–local covers by Cohen-Macaulay and resolution-rational varieties, which are generally not Gorenstein. Finally, we determine the singular loci in the …
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Monomial Ideals, N-Lists, and Smallest Graded Betti Numbers
… our inquiry to the graded betti numbers of Gorenstein ideals attaining H . Finally, we demonstrate with an infinite family that a smallest element may fail to exist even if H is the Hilbert function of an R-sequence.
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A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices
… k a field, and consider homogeneous grade three Gorenstein ideals I in B. The Buchsbaum-Eisenbud structure theorem for grade three Gorenstein algebras such as B/I implies that there exists an alternating presentation matrix psi. In a recent paper, Fisher describes how to produce such an …
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