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81.
Craig Huneke 《Proceedings of the American Mathematical Society》2007,135(7):2003-2005
This note proves that if is an unramified regular local ring and proper ideals of height at least two, then is never Gorenstein.
82.
岑建苗 《宁波大学学报(理工版)》1999,12(2):1-8
研究三角Hopf代数众模范畴上的Lie代数和Lie余代数,主要讨论Lie代数和Lie众代数的对偶.给出了Lie代数的泛包络代数的结构. 相似文献
84.
Astrid Franz 《Mathematische Nachrichten》2001,223(1):23-32
For a special class of non–injective maps on Riemannian manifolds upper and lower bounds for the Hausdorff dimension of invariant sets are given in terms of the singular values of the tangent map. The upper estimation is based on a theorem by Douady and Oesterlé and its generalization to Riemannian manifolds by Noack and Reitmann , but additionally information about the noninjectivity is used. The lower estimation can be reached by modifying a method, derived by Shereshevskij for geometric constructions on the real line (also described by Barreira , for similar constructions in general metric spaces. The upper and lower dimension estimates for k — 1 — endomorphisms can for instance be applied to Julia sets of quadratic maps on the complex plane. 相似文献
85.
令A是阿贝尔范畴, T是A的一个自正交子范畴, 且T中每个对象均有有限投射维数和内射维数. 假设左Gorenstein子范畴lG(T)等于T的右正交类,且右Gorenstein子范畴rG(T)等于T的左正交类,我们证明了Gorenstein子范畴$G(T)$等于T的左正交类与T的右正交类之交,并且证明了它们的稳定范畴三角等价于A关于T的相对奇点范畴.作为应用,令$R$是有有限左自内射维数的左诺特环, $_RC_s$是半对偶化双模,且所有内射左$R$-模的平坦维数的上确界有限, 我们证明了 若$\mbox{}_RC$有有限内射(平坦)维数且$C$的右正交类包含$R$,则存在从$C$-Gorenstein投射模与关于$C$的Bass类的交到关于$C$-投射模的相对奇点范畴间的三角等价,推广了某些经典的结果. 相似文献
86.
Peng YU 《Frontiers of Mathematics in China》2018,13(3):691-713
We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [Math. Ann., 2012, 353: 765–781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras. 相似文献
87.
Molly Dunkum 《Czechoslovak Mathematical Journal》2009,59(1):241-247
There is a classical result known as Baer’s Lemma that states that an R-module E is injective if it is injective for R. This means that if a map from a submodule of R, that is, from a left ideal L of R to E can always be extended to R, then a map to E from a submodule A of any R-module B can be extended to B; in other words, E is injective. In this paper, we generalize this result to the category q
ω consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma is useful in proving that
torsion free covers exist for q
ω.
相似文献
88.
Nan GAO 《数学年刊B辑(英文版)》2009,30(3):231-238
The relative transpose via Gorenstein projective modules is introduced, and some corresponding results on the Auslander-Reiten sequences and the Auslander-Reiten formula to this relative version are generalized. 相似文献
89.
When the base connected cochain DG algebra is cohomologically bounded, it is proved that the difference between the amplitude
of a compact DG module and that of the DG algebra is just the projective dimension of that module. This yields the unboundedness
of the cohomology of non-trivial regular DG algebras.
When A is a regular DG algebra such that H(A) is a Koszul graded algebra, H(A) is proved to have the finite global dimension. And we give an example to illustrate that the global dimension of H(A) may be infinite, if the condition that H(A) is Koszul is weakened to the condition that A is a Koszul DG algebra. For a general regular DG algebra A, we give some equivalent conditions for the Gorensteiness.
For a finite connected DG algebra A, we prove that Dc(A) and Dc(A
op) admit Auslander-Reiten triangles if and only if A and A
op are Gorenstein DG algebras. When A is a non-trivial regular DG algebra such that H(A) is locally finite, Dc(A) does not admit Auslander-Reiten triangles. We turn to study the existence of Auslander-Reiten triangles in Dlfb(A) and Dlfb (A
op) instead, when A is a regular DG algebra.
This work was supported by the National Natural Science Foundation of China (Grant No. 10731070) and the Doctorate Foundation
of Ministry of Education of China (Grant No. 20060246003) 相似文献
90.
Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M).Moreover,cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R). 相似文献