Restricted Homological Dimensions and Cohen–Macaulayness
نویسندگان
چکیده
منابع مشابه
The 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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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 کاملHomological dimensions of complexes of R-modules
Let R be an associative ring with identity, C(R) be the category of com-plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))−)have enough injectives in C(R). As an application, we prove that for each atcomplex F and each complex Y of R-modules, Exti (F,X)= 0, whenever Ris n-perfect and i > n.
متن کاملHomological Dimensions of Ring Spectra
We define homological dimensions for S-algebras, the generalized rings that arise in algebraic topology. We compute the homological dimensions of a number of examples, and establish some basic properties. The most difficult computation is the global dimension of real K-theory KO and its connective version ko at the prime 2. We show that the global dimension of KO is 2 or 3, and the global dimen...
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: 2002
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9115