共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we present some results on the bounded derived category of Artin algebras, and in particular on the indecomposable
objects in these categories, using homological properties. Given a complex X
*, we consider the set and we define the application . We give relationships between some homological properties of an algebra and the respective application l. On the other hand, using homological properties again, we determine two subcategories of the bounded derived category of
an algebra, which turn out to be the bounded derived categories of quasi-tilted algebras. As a consequence of these results
we obtain new characterizations of quasi-tilted and quasi-tilted gentle algebras.
Presented by Raymundo Bautista. 相似文献
2.
Let (R, 𝔪) be a commutative Noetherian local ring. It is known that R is Cohen–Macaulay if there exists either a nonzero finitely generated R-module of finite injective dimension or a nonzero Cohen–Macaulay R-module of finite projective dimension. In this article, we investigate the Gorenstein analogues of these facts. 相似文献
3.
Let R a standard graded algebra over a field k. In this paper, we give a relation in terms of graded Betti numbers, called the Herzog–Kühl equations, for a pure R-module M to satisfy the condition dim(R)?depth(R) = dim(M)?depth(M). When R is Cohen–Macaulay, we prove an analogous result characterizing all graded Cohen–Macaulay R-modules of finite projective dimension. Finally, as an application, we show that the property of R being Cohen–Macaulay is characterized by the existence of pure Cohen–Macaulay R-modules corresponding to any degree sequence of length at most depth(R). 相似文献
4.
Zhi-Wei Li 《代数通讯》2013,41(9):3725-3753
Beligiannis and Marmaridis in 1994, constructed the one-sided triangulated structures on the stable categories of additive categories induced from some homologically finite subcategories. We extend their results to slightly more general settings. As an application of our results, we give some new examples of one-sided triangulated categories arising from abelian model categories. An interesting outcome is that we can describe the pretriangulated structures of the homotopy categories of abelian model categories via those of stable categories. 相似文献
5.
Lukáš Vokřínek 《代数通讯》2013,41(5):2110-2117
We provide a counterexample to a theorem of Ford, namely a pushout square of categories with all involved functors injective, such that there is no associated exact “Mayer–Vietoris” sequence of derived limits. Further, we construct a Mayer–Vietoris sequence for derived (co)limits under some additional hypotheses, extending the well-known case of a pushout square of group monomorphisms. 相似文献
6.
Dao Thanh Ha 《代数通讯》2013,41(3):992-1004
We give bounds for the Castelnuovo–Mumford regularity of the so-called sequentially κ-Buchsbaum modules and of the canonical modules of certain rings. 相似文献
7.
Boris Youssin 《K-Theory》1997,11(4):373-395
We define the notion of cobordism of two objects in a trianulated category, and the Witt group of such category is defined as the Grothendieck group of cobordism classes of self-dual objects. We prove that the Witt group of a t-category is a free Abelian group generated by the classes of irreducible self-dual objects of its heart. In case of derived category of of complexes of sheaves on a stratified space with the middle-perversity t-structure, these irreducibles are local systems on the strata. 相似文献
8.
We generalize results on existence of recollement situations of singularity categories of lower triangular Gorenstein algebras and stable monomorphism categories of Cohen–Macaulay modules. 相似文献
9.
10.
Kohji Yanagawa 《代数通讯》2013,41(8):3122-3146
11.
A characterization of finitely generated torsion modules of not necessarily finite projective dimension over a Cohen–Macaulay ring, is given in terms of the non-Cohen–Macaulay loci and the Fitting invariants of a free resolution of such a module. 相似文献
12.
Somayeh Moradi 《代数通讯》2018,46(8):3377-3387
In this paper, we introduce and study families of squarefree monomial ideals called clique ideals and independence ideals that can be associated to a finite graph. A family of clique ideals with linear resolutions has been characterized. Moreover, some families of graphs for which the quotient ring of their clique ideal is Cohen–Macaulay are introduced and some homological invariants of the clique ideal of a graph G, which is the complement of a path graph or a cycle graph, are obtained. Also some algebraic properties of the independence ideal of path graphs, cycle graphs and chordal graphs are studied. 相似文献
13.
Let 𝕂 be a field, and let R = 𝕂[x 1,…, x n ] be the polynomial ring over 𝕂 in n indeterminates x 1,…, x n . Let G be a graph with vertex-set {x 1,…, x n }, and let J be the cover ideal of G in R. For a given positive integer k, we denote the kth symbolic power and the kth bracket power of J by J (k) and J [k], respectively. In this paper, we give necessary and sufficient conditions for R/J k , R/J (k), and R/J [k] to be Cohen–Macaulay. We also study the limit behavior of the depths of these rings. 相似文献
14.
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16.
本文在L—fuzzy模范畴中,建立了相应的张量积,给出了它的结构性、存在性与唯一性定理,并讨论了张量函子与Hom函子的伴随性。所得结果为通常张量积的“良好推广”(goodextension)。 相似文献
17.
An Auslander-Reiten formula for complexes of modules is presented. This formula contains as a special case the classical Auslander-Reiten formula. The Auslander-Reiten translate of a complex is described explicitly, and various applications are discussed. 相似文献
18.
A left R-module M is called strongly P-projective if Exti(M, P) = 0 for all projective left R-modules P and all i ≥ 1. In this article, we first discuss properties of strongly P-projective modules. Then we introduce and study the strongly P-projective dimensions of modules and rings. The relations between the strongly P-projective dimension and other homological dimensions are also investigated. 相似文献
19.
Roberto Martínez Villa 《代数通讯》2013,41(10):3941-3973
A contravariant functor is constructed from the stable projective homotopy theory of finitely generated graded modules over a finite-dimensional algebra to the derived category of its Yoneda algebra modulo finite complexes of modules of finite length. If the algebra is Koszul with a noetherian Yoneda algebra, then the constructed functor is a duality between triangulated categories. If the algebra is self-injective, then stable homotopy theory specializes trivially to stable module theory. In particular, for an exterior algebra the constructed duality specializes to (a contravariant analog of) the Bernstein–Gelfand–Gelfand correspondence. 相似文献
20.
研究范畴与半群通过幂等元双序建立的一种自然联系.对每个有幂等元的半群S,其幂等元生成的左、右主理想之集通过双序ω~e,ω~r自然确定两个有子对象、有像且每个包含都右可裂的范畴L(S),R(S),其中态射的性质与S中元素的富足性、正则性有自然对应.利用这个联系,我们定义了"平衡(富足、正规)范畴"概念.对任一平衡(富足、正规)范畴■,我们构造其"锥半群"■,证明■左富足(富足、正则),且每个平衡(富足、正规)范畴■都与某左富足(富足、正则)半群S的左主理想范畴L(S)(作为有子对象的范畴)同构. 相似文献