共查询到20条相似文献,搜索用时 15 毫秒
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(11):959-962
We prove a descent theorem for the complete intersection property by homomorphisms of finite (Avramov's) virtual projective dimension. This result suggests a (slight) modification of Avramov's definition of virtual projective dimension. 相似文献
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Tilting modules of finite projective dimension 总被引:18,自引:0,他引:18
Yoichi Miyashita 《Mathematische Zeitschrift》1986,193(1):113-146
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We prove versions of results of Foxby and Holm about modules of finite (Gorenstein) injective dimension and finite (Gorenstein)
projective dimension with respect to a semidualizing module. We also verify special cases of a question of Takahashi and White.
This research was conducted while S.S.-W. visited the IPM in Tehran during July 2008. The research of S.Y. was supported in
part by a grant from the IPM (No. 87130211). 相似文献
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S. P. Dutta 《Proceedings of the American Mathematical Society》2003,131(1):113-116
Recently Avramov and Miller proved that over a local complete intersection ring in characteristic 0$">, a finitely generated module has finite projective dimension if for some 0$"> and for some 0$">, being the frobenius map repeated times. They used the notion of ``complexity' and several related theorems. Here we offer a very simple proof of the above theorem without using ``complexity' at all.
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Z Füredi 《Journal of Combinatorial Theory, Series A》1982,32(1):66-72
Suppose that is a finite set-system of N elements with the property |A ∩ A′| = 0, 1 or k for any two different A, A′ ?A. We show that for N > k14 where equality holds if and only if k = q + 1 (q is a prime power) and is the set of subspaces of dimension at most two of the t-dimensional finite projective space of order q. 相似文献
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Let M be a finitely generated module over a local ring R of characteristic p > 0. If depth(R) = s, then the property that M has finite projective dimension can be characterized by the vanishing of the functor ExtiR(M, fnR){{\rm Ext}^i_R(M, ^{f^n}R)} for s + 1 consecutive values i > 0 and for infinitely many n. In addition, if R is a d-dimensional complete intersection, then M has finite projective dimension can be characterized by the vanishing of the functor ExtiR(M, fnR){{\rm Ext}^i_R(M, ^{f^n}R)} for some i ≥ d and some n > 0. 相似文献
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Jinjia Li 《Proceedings of the American Mathematical Society》2006,134(5):1271-1275
Let be a finitely generated module over a local complete intersection of characteristic . The property that has finite projective dimension can be characterized by the vanishing of for some and for some .
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Claudia Miller 《Mathematische Zeitschrift》2000,233(1):127-136
Let M be a module of finite length over a complete intersection (R,m) of characteristic . We characterize the property that M has finite projective dimension in terms of the asymptotic behavior of a certain length function defined using the Frobenius
functor. This may be viewed as the converse to a theorem of S. Dutta. As a corollary we get that, in a complete intersection
(R,m), an m-primary ideal I has finite projective dimension if and only if its Hilbert-Kunz multiplicity equals the length of R/I.
Received June 22, 1998; in final form October 13, 1998 相似文献
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Luchezar L. Avramov Vesselin N. Gasharov Irena V. Peeva 《Publications Mathématiques de L'IHéS》1997,86(1):67-114
A new homological invariant is introduced for a finite module over a commutative noetherian ring: its CI-dimension. In the
local case, sharp quantitative and structural data are obtained for modules of finite CI-dimension, providing the first class
of modules of (possibly) infinite projective dimension with a rich structure theory of free resolutions.
The first author was partly supported by NSF Grant No. DMS-9102951. 相似文献
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We prove rigidity type results on the vanishing of stable Ext and Tor for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of pre-rigidity, which generalizes phenomena for modules of finite complete intersection dimension and complexity one. Using this concept, we prove results on length and vanishing of homology modules. 相似文献
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Oana Veliche 《Transactions of the American Mathematical Society》2006,358(3):1257-1283
We define and study a notion of Gorenstein projective dimension for complexes of left modules over associative rings. For complexes of finite Gorenstein projective dimension we define and study a Tate cohomology theory. Tate cohomology groups have a natural transformation to classical Ext groups. In the case of module arguments, we show that these maps fit into a long exact sequence, where every third term is a relative cohomology group defined for left modules of finite Gorenstein projective dimension.