共查询到18条相似文献,搜索用时 484 毫秒
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作者定义了Gorenstein AC导出范畴 Dbgac(R)并且和导出范畴作了一些比较.作者定义了Gorenstein AC奇点范畴 Dbgacsg(R),在这个范畴中具有有限Gorenstein AC- 投射维数的模都是零对象.同时, 作者给出了由Gorenstein AC- 投射模构成的稳定范畴到奇点范畴的三角嵌入 F : GAC → Dbsg(R) .通过作函子 F 的商引入Gorenstein AC亏范畴 Dbgacd(R),并且给出三角等价 Dbgacd(R) = Dbgacsg(R) 相似文献
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We introduce the singularity category with respect to Ding projective modules, D_(dpsg)~b(R),as the Verdier quotient of Ding derived category D_(DP)~b(R) by triangulated subcategory K~b(DP), and give some triangle equivalences. Assume DP is precovering. We show that D_(DP)~b(R)≌K~(-,dpb)(DP)and D_(dpsg)~b(R)≌D_(Ddefect)~b(R). We prove that each R-module is of finite Ding projective dimension if and only if D_(dpsg)~b(R) = 0. 相似文献
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令R是左Gorenstein环.我们构造了奇点反导出模型范畴和奇点余导出模型范畴(见文[Models for singularity categories,Adv Math.,2014,254:187-232])之间的Quillen等价.作为应用,给出了投射,内射模的正合复形的同伦范畴之间的一个具体的等价■. 相似文献
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证明了三角范畴的recollement可以自然诱导其商范畴的recollement.特别地,得到类似于群同态第二基本定理的结果,即若U是三角范畴D的局部化(或余局部化)子范畴,V是U的三角满子范畴,则U/V是D/V的局部化(或余局部化)子范畴,并且有三角等价(D/V)/(U/V)≌D/U.同理,对Abel范畴的recollement也有相应的结果. 相似文献
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本文研究了外三角范畴中相对合冲对象和粘合R(A’,A,A")中相对合冲对象的保持问题.利用相对同调的方法,获得了相对合冲对象的一些性质和它的等价刻画,推广了阿贝尔范畴和三角范畴中一些结果,给出了相对投射维数的一个等价刻画.主要证明了:在满足一定条件时,A’和A"中的相对合冲对象可以诱导出A中的相对合冲对象.反之,对于A中的相对合冲对象也可以诱导出A’和A"中的相对合冲对象. 相似文献
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光滑映射芽的有限决定性是奇点理论中一个重要专题 .对函数芽的有限决定性问题 ,主要是在右等价群及其一些子群作用下来讨论的 .本文在 [1]和 [4 ]的基础上讨论函数芽在右等价群的正规子群 R*n (S;n)作用下的有限决定性 ,并组出函数芽有限 R*r (S;n) -决定的一个充分必要条件 . 相似文献
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引入了Koszul微分分次模的概念. 给定Koszul微分分次代数上的一个下有界的微分分次模, 如果这个模到平凡模的Ext-\!群是有界的分次空间, 则它必定包含一个微分分次子模, 其在适当的截断和移位下是Koszul微分分次模; 这样的模还可以通过一系列Koszul微分分次模来逼近(参见本文推论3.6). 设$A$是一个Koszul微分分次代数, $D^c(A)$是微分分次右$A$-\!模范畴的导出范畴中由对象$A_A$生成的满三角子范畴. 如果平凡微分分次模$k_A$落在范畴$D^c(A)$中, 则三角范畴$D^c(A)$的标准$t$-\!结构的中心, 作为Abel范畴, 与某个有限维代数上的有限生成模范畴对偶. 进一步, 可推得三角范畴$D^c(A)$等价于它的标准$t$-\!结构的中心的有界导出范畴. 相似文献
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In this paper, we study the homotopy category of unbounded complexes of strongly copure projective modules with bounded relative homologies K~(∞,bscp)(SCP).We show that the existence of a right recollement of K~(∞,bscp)(SCP) with respect to K~(-,bscp)(SCP), K_(scpac)(SCP) and K~(∞,bscp)(SCP) has the homotopy category of strongly copure projective acyclic complexes as a triangulated subcategory in some case. 相似文献
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R. G. Larson 《Applied Categorical Structures》1998,6(2):139-150
The relation between a monoidal category which has an exact faithful monoidal functor to a category of finite rank projective modules over a Dedekind domain, and the category of continuous modules over a topological bialgebra is discussed. If the monoidal category is braided, the bialgebra is topologically quasitriangular. If the monoidal category is rigid monoidal, the bialgebra is a Hopf algebra. 相似文献
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Using categorical techniques we obtain some results on localization and colocalization theory in Grothendieck categories with a set of small projective generators. In particular, we give a sufficient condition for such category to be semiartinian. For semiartinian Grothendieck categories where every simple object has a projective cover, we obtain that every localizing subcategory is a TTF-class. In addition, some applications to semiperfect categories are obtained. 相似文献
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For a finite free and projective EI category, we prove that Gorenstein-projective modules over its category algebra are closed under the tensor product if and only if each morphism in the given category is a monomorphism. 相似文献
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Fan Kong 《Algebras and Representation Theory》2014,17(4):1289-1301
We find sufficient and necessary conditions for the category of Gorenstein projective modules of an artin algebra being an abelian category, and give another proof for the Auslander–Solberg correspondence which demonstrates the concrete form of the category of Gorenstein projective modules. Then we find a characterization for this category of Gorenstein projective modules. At last we give an example of this correspondence. 相似文献
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In analogy with classical projective algebraic geometry, Hilbert functors can be defined for objects in any Abelian category. We study the moduli problem for such objects. Using Grothendieck's general framework. We show that with suitable hypotheses the Hilbert functor is representable by an algebraic space locally of finite type over the base field. For the category of the graded modules over a strongly Noetherian graded ring, the Hilbert functor of graded modules with a fixed Hilbert series is represented by a commutative projective scheme. For the projective scheme corresponding to a suitable noncommutative graded algebra, the Hilbert functor is represented by a countable union of commutative projective schemes. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(12):107145
The singularity category of a ring makes only the modules of finite projective dimension vanish among the modules, so that the singularity category is expected to characterize a homological property of modules of infinite projective dimension. In this paper, among such modules, we deal with eventually periodic modules over a left artin ring, and, as our main result, we characterize them in terms of morphisms in the singularity category. As applications, we first prove that, for the class of finite dimensional algebras over a field, being eventually periodic is preserved under singular equivalence of Morita type with level. Moreover, we determine which finite dimensional connected Nakayama algebras are eventually periodic when the ground field is algebraically closed. 相似文献