共查询到20条相似文献,搜索用时 531 毫秒
1.
In this paper we provide a classification theorem and a structure theorem for exact differential graded algebras, and we use the classification theorem to show that a differential graded algebra A is semisimple (as a differential graded algebra) precisely when the graded algebra Z(A) is semisimple (as a graded algebra) and A is an exact complex. We also relate exact differential graded algebras with a graded version of Hochschild cohomology. 相似文献
2.
本文研究了群分次环的有限正规分次扩张问题.利用经典环论方法,得到一个群分次环与其有限正规分次扩张环之间关于分次Jacobson根和分次素根的关系,同时,给出了分次情形的Cutting down定理和Lying over定理. 相似文献
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4.
In this paper, a super version of the Hopf quiver theory is developed. The notion of Hopf superquivers is introduced. It is
shown that only the path supercoalgebras of Hopf superquivers admit graded Hopf superalgebra structures. A complete classification
of such graded Hopf superalgebras is given. A superquiver setting for general pointed Hopf superalgebras is also built up.
In particular, a super version of the Gabriel type theorem and the Cartier-Gabriel decomposition theorem is given. 相似文献
5.
Mark V. Losik 《Annals of Global Analysis and Geometry》1995,13(4):323-338
The complex ofG-invariant forms and its cohomology for arbitraryG-manifolds and especially for a certain class ofG-manifolds, which are locally trivial fiber bundles over the orbit space, are considered. The transgression in the differential graded algebra of basic elements for tensor product of two identical Weil algebras of a reductive Lie groupG is calculated. This is used to get two convenient differential graded algebras with the same minimal models as the differential algebra of differential forms on the cross product of two principalG-bundles overG and ofG-invariant forms onG-manifolds of the above class. In particular, for compactG the generalization of the Cartan theorem on the cohomology of a homogeneous space is proved.Partially supported by the grant of the AMS's fSU Aid Fund 相似文献
6.
In this article we introduce a certain family of graded modules associated to a given module. These modules provide a natural extension of the notion of the associated graded ring of an ideal. We will investigate their properties. In particular, we will try to extend Ree' theorem on the associated graded ring of an ideal generated by a regular sequence to this context. 相似文献
7.
8.
Catriona Maclean 《Mathematische Nachrichten》2019,292(1):121-126
In 2 , Huayi Chen introduces the notion of an approximable graded algebra, which he uses to prove a Fujita‐type theorem in the arithmetic setting, and asks if any such algebra is a sub‐algebra of the graded section ring of a big line bundle on an algebraic variety. We give a counter‐example showing that this is not the case. 相似文献
9.
《Journal of Pure and Applied Algebra》2023,227(2):107180
A silting theorem was established by Buan and Zhou as a generalisation of the classical tilting theorem of Brenner and Butler. In this paper, we give an alternative proof of the theorem by using differential graded algebras. 相似文献
10.
A. L. Kanunnikov 《Moscow University Mathematics Bulletin》2013,68(3):162-165
We continue the study of graded Goldie rings and their quotient rings. The main results are inverse Goldie’s theorem for graded rings and graded analogs of third Goldie’s theorem. 相似文献
11.
In this paper, we give a simpler proof of the Golubchik–Mikhalev–Zelmanov theorem on the structure of isomorphisms between
general linear groups over associative rings, and also prove an extension of this theorem for linear groups over rings graded
by an Abelian group. 相似文献
12.
13.
LIU Gongxiang & YE Yu Institute of Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2006,49(3):320-329
In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n) are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras. 相似文献
14.
I. N. Balaba S. V. Limarenko A. V. Mikhalev S. V. Zelenov 《Journal of Mathematical Sciences》2005,128(6):3350-3364
The main purpose of this paper is to prove three density theorems for rings graded by semigroups and modules graded by acts over these semigroups with some cancellation conditions. In addition, the density theorem for superrings and supermodules is proved.__________Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 27–49, 2003. 相似文献
15.
Pierre Lorenzon 《manuscripta mathematica》2000,101(3):271-299
After discussing gradings by sheaves of degrees, we associate to any log scheme a canonical invertible sheaf endowed with
a certain multiplicative structure, which we call its associated graded algebra. In the relative case we construct a canonical
connection on this algebra. In the log smooth case over a base of positive characteristic p, we study integrable and p-integrable
graded modules over this algebra, and establish a Cartier type p-descent theorem, generalizing previous results of Ogus.
We apply it to give an alternate proof of a result of Tsuji on closed forms fixed by the Cartier operator
Received: 15 January 1999 / Revised version: 30 September 1999 相似文献
16.
陆仲坚 《纯粹数学与应用数学》2001,17(2):175-179
首先给出了 gr-正则环为分次除环的两个充要条件 ,其次讨论了分次正则环r G(R)和分次 Jacobson根 JG(R)之间的关系 ,最后给出了分次 Abel正则环的结构定理 . 相似文献
17.
Luchezar L. Avramov Ragnar-Olaf Buchweitz Srikanth Iyengar 《Inventiones Mathematicae》2007,169(1):1-35
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules
over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class – a substitute
for the length of a free complex – and on the rank of a differential module in terms of invariants of its homology. These
results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization
of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes
over commutative noetherian rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings. 相似文献
18.
N. A. Koreshkov 《Mathematical Notes》2007,82(3-4):321-331
In the paper, an analog of the Engel theorem for graded algebras admitting a Lie-type module is proved. Moreover, it is shown that every semisimple algebra of associative type with ordered grading and one-dimensional grading subspaces is the direct sum of two-sided ideals that are simple algebras. 相似文献
19.
The reduced Whitehead group SK1 of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here
are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following
two theorems: It is proved that SK1 of a tame valued division algebra over a henselian field coincides with SK1 of its associated graded division algebra. Furthermore, it is shown that SK1 of a graded division algebra is isomorphic to SK1 of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain
valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups,
and also describes SK1 for generic abelian crossed products. 相似文献
20.
Emil Ilić-Georgijević 《代数通讯》2017,45(9):3886-3891
In this paper, we study the graded Thierrin radical and the classical Thierrin radical of a graded ring, which is the direct sum of a family of its additive subgroups indexed by a nonempty set, under the assumption that the product of homogeneous elements is again homogeneous. There are two versions of this graded radical, the graded Thierrin and the large graded Thierrin radical. We establish several characterizations of the graded Thierrin radical and prove that the largest homogeneous ideal contained in the classical Thierrin radical of a graded ring coincides with the large graded Thierrin radical of that ring. 相似文献