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1.
Jinde Xu  Panyue Zhou 《代数通讯》2013,41(12):5168-5182
Let 𝒳 ? 𝒜 be subcategories of a triangulated category 𝒯, and 𝒳 a functorially finite subcategory of 𝒜. If 𝒜 has the properties that any 𝒳-monomorphism of 𝒜 has a cone and any 𝒳-epimorphism has a cocone, then the subfactor category 𝒜/[𝒳] forms a pretriangulated category in the sense of [4 Beligiannis , A. , Reiten , I. ( 2007 ). Homological and Homotopical Aspects of Torsion Theories . Memoirs of the AMS 883 : 426454 . [Google Scholar]]. Moreover, the above pretriangulated category 𝒜/[𝒳] with 𝒯(𝒳, 𝒳[1]) = 0 becomes a triangulated category if and only if (𝒜, 𝒜) forms an 𝒳-mutation pair and 𝒜 is closed under extensions.  相似文献   

2.
We consider a homology theory on a triangulated category with values in an abelian category. If the functor h reflects isomorphisms, is full and is such that for any object x in there is an object X in with an isomorphism between h(X) and x, we prove that is a hereditary abelian category, all idempotents in split and the kernel of h is a square zero ideal which as a bifunctor on is isomorphic to. The second author is a researcher from CONICET, Argentina.  相似文献   

3.
Hiroyuki Nakaoka 《代数通讯》2013,41(10):4302-4326
In this article, we investigate the condition for the hearts of twin cotorsion pairs to be equivalent, compatibly with the associated functors. This is related to the vanishing of components of pairs through the associated functors.  相似文献   

4.
三角范畴是一个带有自同构且满足四条公理的加法范畴,其中的一条重要公理就是八面体公理,该公理形式复杂不易理解难以应用.在本文中,作者讨论了三角范畴定义中八面体公理的几个等价命题,给出了新的八面体公理的等价命题,证明了各个公理间的相互等价关系,同时简化了八面体的表达形式,并且给出了该定理的一个具体应用.  相似文献   

5.
Jinde Xu  Panyue Zhou 《代数通讯》2013,41(7):2732-2746
A notion of mutation pairs of subcategories in an abelian category is defined in this article. For an extension closed subcategory 𝒵 and a rigid subcategory 𝒟 ? 𝒵, the subfactor category 𝒵/[𝒟] is also a triangulated category whenever (𝒵, 𝒵) forms a 𝒟-mutation pair. Moreover, if 𝒟 and 𝒵 satisfy certain conditions in modΛ, the category of finitely generated Λ-modules over an artin algebra Λ, the triangulated category 𝒵/[𝒟] has a Serre functor.  相似文献   

6.
Panyue Zhou  Jinde Xu 《代数通讯》2013,41(8):3498-3514
Let 𝒞 be a triangulated category. When ω is a functorially finite subcategory of 𝒞, Jøtrgensen showed that the stable category 𝒞/ω is a pretriangulated category. A pair (𝒳, 𝒴) of subcategories of 𝒞 with ω ? 𝒳 ∩ 𝒴 gives rise to a pair (𝒳/ω, 𝒴/ω) of subcategories of 𝒞/ω. In this article, we find conditions for (𝒳/ω, 𝒴/ω) to be a torsion pair in terms of properties of the pair (𝒳, 𝒴). In particular, we obtain necessary and sufficient conditions for (𝒳/ω, 𝒴/ω) to be a torsion pair in the stable category 𝒞/ω when τω = ω, where τ is the Auslander–Reiten translation.  相似文献   

7.
设■是阿贝尔范畴,■是■的子范畴.Sather-Wagstaff, Sharif和White引入了Gorenstein子范畴的概念,记为■.我们用■(相应地,■)代表纯投射R-模类(相应地,投射R-模类).本文给出了一类满足条件"■"的环,由此给出了当■是■的子范畴时,■是否包含在■中的一个否定回答.进一步,刻画了包含关系■和■何时成立.  相似文献   

8.
Pin Liu 《代数通讯》2013,41(10):4296-4307
This note investigates the modules over the endomorphism algebras of maximal rigid objects in 2-Calabi-Yau triangulated categories. We study the possible complements for almost complete tilting modules. Combining with Happel's theorem, we show that the possible exchange sequences for tilting modules over such algebras are induced by the exchange triangles for maximal rigid objects in the corresponding 2-Calabi-Yau triangulated categories. For the modules of infinite projective dimension, we generalize a recent result by Beaudet–Brüstle–Todorov for cluster-tilted algebras.  相似文献   

9.
The flag geometry =( ) of a finite projective plane of order s is the generalized hexagon of order (s, 1) obtained from by putting equal to the set of all flags of , by putting equal to the set of all points and lines of and where I is the natural incidence relation (inverse containment), i.e., is the dual of the double of in the sense of Van Maldeghem Mal:98. Then we say that is fully and weakly embedded in the finite projective space PG(d, q) if is a subgeometry of the natural point-line geometry associated with PG(d, q), if s = q, if the set of points of generates PG(d, q), and if the set of points of not opposite any given point of does not generate PG(d, q). Preparing the classification of all such embeddings, we construct in this paper the classical examples, prove some generalities and show that the dimension d of the projective space belongs to {6,7,8}.  相似文献   

10.
We study the category 𝒞(X, Y) generated by an exceptional pair (X, Y) in a hereditary category ?. If r = dim k Hom(X, Y) ≥ 1 we show that there are exactly 3 possible types for 𝒞(X, Y), all derived equivalent to the category of finite dimensional modules mod(H r ) over the r-Kronecker algebra H r . In general 𝒞(X, Y) will not be equivalent to a module category. More specifically, if ? is the category of coherent sheaves over a weighted projective line 𝕏, then 𝒞(X, Y) is equivalent to the category of coherent sheaves on the projective line ?1 or to mod(H r ) and, if 𝕏 is wild, then every r ≥ 1 can occur in this way.  相似文献   

11.
Let be a triangulated category with coproducts, the full subcategory of compact objects in . If is the homotopy category of spectra, Adams (Topology 10 (1971) 185–198), proved the following: All homological functors are the restrictions of representable functors on , and all natural transformations are the restrictions of morphisms in . It has been something of a mystery, to what extent this generalises to other triangulated categories. In Neeman (Topology 36 (1997) 619–645), it was proved that Adams’ theorem remains true as long as is countable, but can fail in general. The failure exhibited was that there can be natural transformations not arising from maps in . A puzzling open problem remained: Is every homological functor the restriction of a representable functor on ? In a recent paper, Beligiannis (Relative homological and purity in triangulated categories, 1999, preprint) made some progress. But in this article, we settle the problem. The answer is no. There are examples of derived categories of rings, and homological functors which are not restrictions of representables.  相似文献   

12.
Aimin Xu 《代数通讯》2013,41(10):3793-3804
We show that an iteration of the procedure used to define the Gorenstein projective modules over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective left R-modules G = … → G 1 → G 0 → G 0 → G 1 → … such that the complex Hom R (G, H) is exact for each projective left R-module H, the module Im(G 0 → G 0) is Gorenstein projective. We also get similar results for Gorenstein flat left R-modules when R is a right coherent ring. As applications, we obtain the corresponding results for Gorenstein complexes.  相似文献   

13.
Let H be a subgroup of a cyclic Singer group of PG (n,q). In this paper we study the following problem: When is a point orbit of H a cap? A necessary and sufficient condition for this is derived and used to give a short proof of some results by Ebert [6] and to show that small orbits are typically caps.  相似文献   

14.
众所周知,Assem-SmalΦ定理在倾斜理论中有重要的作用.本文的目的是建立一个在余模范畴中的Assem-SmalΦ定理的版本,并通过利用预包络理论来刻画余模范畴中的余倾斜挠类.  相似文献   

15.
Our aim in this paper is to develop a theory of purity and to prove in a unified conceptual way the existence of almost split morphisms, almost split sequences and almost split triangles in abstract homotopy categories, a rather omnipresent class of categories of interest in representation theory. Our main tool for doing this is the classical Brown representability theorem.  相似文献   

16.
Let be a projective space. In this paper we consider sets of planes of such that any two planes of intersect in exactly one point. Our investigation will lead to a classification of these sets in most cases. There are the following two main results:- If is a set of planes of a projective space intersecting mutually in one point, then the set of intersection points spans a subspace of dimension 6. There are up to isomorphism only three sets where this dimension is 6. These sets are related to the Fano plane.- If is a set of planes of PG(d,q) intersecting mutually in one point, and if q3, 3(q2+q+1), then is either contained in a Klein quadric in PG(5,q), or is a dual partial spread in PG(4,q), or all elements of pass through a common point.  相似文献   

17.
复射影空间中的完备全实伪脐子流形   总被引:2,自引:0,他引:2  
Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn+p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem such that Mn becomes totally umbilical submanifold and improve the related results.  相似文献   

18.
关于复射影空间中的全实伪脐子流形   总被引:2,自引:1,他引:1  
设$M^n$是复射影空间${\bf C}P^{n+p}$中的全实子流形. 本文研究$M^n$的平行脐性法向量场在法丛中的位置. 在$p>0$的情形通过选取合适的标架场, 得到具有平行平均曲率向量的全实伪脐子流形关于第二基本形式模长平方的一个Pinching定理.  相似文献   

19.
Manoj K. Yadav 《代数通讯》2013,41(9):3350-3354
Let G be a finite group and M(G) be the subgroup of G generated by all noncentral elements of G that lie in the conjugacy classes of the smallest size. Recently several results have been proved regarding the nilpotency class of M(G) and F(M(G)), where F(M(G)) denotes the Fitting subgroup of M(G). We prove some conditional results regarding the nilpotency class of M(G).  相似文献   

20.
In a locally presentable category seen as a concrete category of structures, we describe the subobjects (resp. the regular, strong subobjects) generated by a subset, first in terms of closure under certain types of implicit partial operations, and then in syntactic terms. This characterizes in particular the locally presentable categories in which various sorts of monos and epis coincide.  相似文献   

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