Coherent Rings and Homologically Finite Subcategories.
نویسندگان
چکیده
منابع مشابه
Contravariantly Finite Resolving Subcategories over Commutative Rings
Contravariantly finite resolving subcategories of the category of finitely generated modules have been playing an important role in the representation theory of algebras. In this paper we study contravariantly finite resolving subcategories over commutative rings. The main purpose of this paper is to classify contravariantly finite resolving subcategories over a henselian Gorenstein local ring;...
متن کاملRings That Are Homologically of Minimal Multiplicity
Let R be a local Cohen-Macaulay ring with canonical module ωR. We investigate the following question of Huneke: If the sequence of Betti numbers {β i (ωR)} has polynomial growth, must R be Gorenstein? This question is well-understood when R has minimal multiplicity. We investigate this question for a more general class of rings which we say are homologically of minimal multiplicity. We provide ...
متن کاملThick Subcategories of Modules over Commutative Rings
For a commutative noetherian ring A, we compare the support of a complex of A-modules with the support of its cohomology. This leads to a classification of all full subcategories of A-modules which are thick (that is, closed under taking kernels, cokernels, and extensions) and closed under taking direct sums.
متن کاملOn n-coherent rings, n-hereditary rings and n-regular rings
We observe some new characterizations of $n$-presented modules. Using the concepts of $(n,0)$-injectivity and $(n,0)$-flatness of modules, we also present some characterizations of right $n$-coherent rings, right $n$-hereditary rings, and right $n$-regular rings.
متن کاملExtensions of covariantly finite subcategories
Gentle and Todorov proved that in an abelian category with enough projective objects, the extension subcategory of two covariantly finite subcategories is covariantly finite. We give an example to show that Gentle–Todorov’s theorem may fail in an arbitrary abelian category; however we prove a triangulated version of Gentle–Todorov’s theorem which holds for arbitrary triangulated categories; we ...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1995
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-12558