منابع مشابه
Homological Dimensions and Regular Rings
A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.
متن کاملGorenstein Homological Dimensions of Commutative Rings
The classical global and weak dimensions of rings play an important role in the theory of rings and have a great impact on homological and commutative algebra. In this paper, we define and study the Gorenstein homological dimensions of commutative rings (Gorenstein projective, injective, and flat dimensions of rings) which introduce a new theory similar to the one of the classical homological d...
متن کاملCharacterizing Local Rings via Homological Dimensions and Regular Sequences Shokrollah Salarian, Sean Sather-wagstaff, and Siamak Yassemi
Let (R, m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If GC -dimension of M/aM is finite for all ideals a generated by an R-regular sequence of length at most d − t then either GC -dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.
متن کاملGorenstein homological dimensions with respect to a semi-dualizing module over group rings
Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring . It is shown that Gorenstein homological dimensions of an -RΓ module M with respect to a semi-dualizing module, are equal over R and RΓ .
متن کاملThe behavior of homological dimensions
Let R be a commutative noetherian ring. We study the behavior of injectiveand at dimension of R-modules under the functors HomR(-,-) and -×R-.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.08.006