Gorenstein平坦(余挠)维数和Hopf作用（英文）

设H是域k上的有限维Hopf代数,A是左H-模代数.本文研究了Gorenstein平坦(余挠)维数在A-模范畴和A#H-模范畴之间的关系.利用可分函子的性质,证明了(1)设A是右凝聚环,若A#H/A可分且φ:A→A#H是可裂的(A,A)-双模同态,则l.Gwd(A)=l.Gwd(A#H);(2)若A#H/A可分且φ:A→A#H是可裂的(A,A)-双模同态,则l.Gcd(A)=l.Gcd(A#H),推广了斜群环上的结果.     

形式三角矩阵环上强Gorenstein平坦模

设Γ是由环R、S和双模SMR组成的形式三角矩阵环.主要讨论环Γ上的模、模同态、模正合列以及模复形.研究了强Gorenstein平坦Γ-模的若干性质及等价刻画,并证明了由模RX和SY以及左-S同态φ:M⊗RX→Y组成的Γ-模是强Gorenstein平坦模,当且仅当RX和SCokerφ均是强Gorenstein平坦模且φ为单同态.     

Hopf代数的冲积的弱整体维数

设H是有限维Hopf代数,A是交换的H-模代数。当H~*是幺模且A中存在迹为1的元素时,本文证明冲积A#H与代数A的弱整体维数相等。     

关于半对偶化模的Gorenstein模的稳定性

本文研究了相对于半对偶化模C的Gorenstein模（即Gorenstein C-投射模,Gorenstein C-内射模和Gorenstein C-平坦模）的稳定性的问题.利用同调的方法,获得了Gorenstein C-投射（C-内射,C-平坦）模具有很好的稳定性的结果,推广了Gorenstein投射（内射,平坦）模具有很好的稳定性的结果.     

弱总体维数和模的自同态

本文用模的自同态,给出弱总体维数≤ｎ的环的特征,其中ｎ≥０．设Ｒ为环,部分地回答了下列问题：何时任意有限表现Ｒ－模Ｍ有无穷分解：０→Ｍ→Ｆ₀→Ｆ₁→…→Ｆ_n→…,其中每个Ｆ_i均是有限生成投射的,ｉ＝１,２,…？     

Gorenstein平坦模与Frobenius扩张

设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的.     

Gorenstein环上的Gorenstein平坦和内射

设R是一个Gorenstein环. 证明了, 如果I是R的一个理想且使得R/I是一个半单环, 则R/I作为右R-模的Gorenstein平坦维数与R/I作为左R-模的Gorenstein内射维数是相等的. 另外证明了, 如果R→S是一个环同态且_SE是左S-模范畴的一个内射余生成元, 则S作为右R-模的Gorenstein平坦维数与E作为左R-模的Gorenstein内射维数是相等的. 同时给出了这些结果的一些应用.     

Δ-tame拟遗传代数

设(K, M, H)是上三角双模问题, Brüstle 和Hille证明了(K, M, H)的矩阵范畴Mat((K, M)的投射生成子P 的自同态代数的反代数A是拟遗传代数, 而且代数A的Δ 好模范畴与Mat((K, M)等价. 本文基于双模问题的tame定理, 证明了如果由上三角双模问题所对应的拟遗传代数A是Δ-tame表示型的, 则 F(Δ)具有齐次性质, 即F(Δ)中的几乎所有的模都同构于它的Auslander-Reiten变换; 进一步地, 如果(K, M, H)是上三角双分双模问题, 则A是Δ-tame表示型的当且仅当 F(Δ)具有齐次性质.     

Smash积的复杂度

给定任意一个有限维代数A,记其复杂度为C（A）.本文的主要结果是：如果有限维Hopf代数H和H是半单的,则对任意有限维H-模代数A,有C（A#H）=C（A）.利用此等式,可以计算一些代数的复杂度.     

顶点算子超代数及相关的结合代数的表示

设 V 是一个顶点算子超代数. 该文得到了一系列的结合代数A_n(V)(对任何n∈ 1/2 + Z₊(i∈ {0,1})). 也给出了A_n(V) -模但非A_n-1/2(V) -模的不可约模范畴和单的可容许的V -模的范畴之间的一一对应关系. 对于给定的A_n(V) -模但非A_n-1/2(V) -模U, 还构造了一类广义Verma可容许的V -模M_n(U). 进而利用结合代数的表示进一步研究了顶点算子超代数的表示论.     

Gorenstein同调维数和环变换

In this paper,we shall be concerned with what happens of Gorenstein homological dimensions when certain modifications are made to a ring.The five structural operations addressed later are the formation of excellent extensions,localizations,Morita equivalences,polynomial extensions and power series extensions.     

Gorenstein tilting pairs

Abstract

Let A be an n-Gorenstein ring. Employing the theory developed by Enochs on the existence of Gorenstein preenvelopes and precovers, we introduce the concept of Gorenstein tilting pair. Moreover, we give a simple characterization on Gorenstein tilting pair, which shows that Gorenstein cotilting and tilting modules are special examples of Gorenstein tilting pair.     

Coherent Rings and Gorenstein FP-Injective Modules

In this article, Gorenstein FP-injective modules are introduced and investigated. A left R-module M is called Gorenstein FP-injective if there is an exact sequence … → E ₁ → E ₀ → E ⁰ → E ¹ → … of FP-injective left R-modules with M = ker(E ⁰ → E ¹) such that Hom _R (P, ?) leaves the sequence exact whenever P is a finitely presented left R-module with pd _R (P) < ∞. Some properties of Gorenstein FP-injective modules are obtained. Several well-known classes of rings are characterized in terms of Gorenstein FP-injective modules.     

模的强Gorenstein平坦维数

In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat and Gorenstein FP-injective dimensions, and show that some characterizations similar to Gorenstein homological dimensions hold for these two dimensions.     

Gorenstein n-X-Injective and n-X-Flat Modules with Respect to a Special Finitely Presented Module

Let R be a ring,X a class of R-modules and n ≥ 1 an integer.We intro-duce the concepts of Gorenstein n-X-injective and n-X-flat modules via special finitely presented modules.Besides,we obtain some equivalent properties of these modules on n-X-coherent rings.Then we investigate the relations among Gorenstein n-X-injective,n-X-flat,injective and fiat modules on X-FC-rings (i.e.,self n-X-injective and n-X-coherent rings).Several known results are generalized to this new context.     

Gorenstein范畴上的一个问题

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.     

Gorenstein fp-平坦和强Gorenstein fp-平坦模

引入了Gorenstein fp-平坦模和强Gorenstein fp-平坦模的概念,讨论了这两类模的一些性质、联系以及稳定性.     

Gorenstein injective envelopes and covers over two sided noetherian rings

We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the connection between the Gorenstein injective modules and the strongly cotorsion modules. We prove that when the ring R is commutative noetherian of finite Krull dimension, the class of Gorenstein injective modules coincides with that of strongly cotorsion modules if and only if the ring R is in fact Gorenstein.     

Gorenstein Modules over Zariski Filtered Rings

Abstract

We study Gorenstein injective and projective modules over Zariski filtered rings and obtain relations between the Gorenstein dimensions on the category of filtered modules from the associated category of graded modules over the associated graded ring.     

Notes on Divisible and Torsionfree Modules

In this article, we first study the existence of envelopes and covers by modules of finite divisible and torsionfree dimensions. Then we investigate divisible and torsionfree dimensions as well as localizations of divisible and torsionfree modules over commutative rings. Finally, Gorenstein divisible and torsionfree modules are introduced and studied.