共查询到19条相似文献,搜索用时 62 毫秒
1.
本文研究了弱模代数上的弱Galois扩张问题,利用不变子函子与积分方法,获得了弱Galois扩张的一个充分必要条件,推广了Cohen,Fishman和Montgomery的对应结果. 相似文献
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设∧是其中心C_∧上的有限维单代数,F是满足C_∧的∧的子环,G是保持Γ的元素不变的∧的自同构的有限群.本文证明:若∧/Γ是G-Galois扩张,则在∧中的中心化子△是C_Γ一分离代数且∧/Γ是Frobenius扩张,这里C_Γ是Γ的中心. 相似文献
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设H是域k上任意的Hopf代数。本文首先讨论了右H_扩张A/A ̄(coH)与Hopf模范畴,给出了A/A ̄(coH)为右H-Galois扩张的充分必要条件和Hopf模范畴满足结构定理的若干等价条件.然后我们讨论了不可约作用与除环的Galois扩张. 相似文献
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陈惠香 《数学年刊A辑(中文版)》1998,(3)
设Hopf代数H余作用于代数A.本文讨论代数A,余不变子代数AcoH及Smash积A#H的相互关系.同时将研究Hopf模,全积分及除环的HopfGalois扩张. 相似文献
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设 H是域 k上的有限维 Hopf代数,K为 H的任意子 Hopf代数,A是右 H-余模代数.设 =(H/K+ H)*和,且有 c∈A,t ·c=1.本 文刻划了 A作为 A# *-模的投射性且证明了:如果A/AH*是 H-Frobenius扩张, 则 A /AH*是 K-Frobenius扩张;如果 A/AH*是 H-Galois扩张,则 A */AH*是 K-Galois扩张. 相似文献
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在本文中引入了泛代数的二次扩张的概念,解决了TU-EC(A)和UT-EC(A)的存在、真类和基数问题,范畴TU-EC(A)(及UT-EC(A)),并得到了有关二次扩张的几个同构定理,还对一点二次扩张作了讨论。 相似文献
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H-弱余模余代数和交叉余积 总被引:3,自引:0,他引:3
王栓宏 《数学年刊A辑(中文版)》1995,(4)
引进了交叉积的对偶交叉余积,证明了:余Cleft模余代数的结构定理(作为余代数);如果为Hopf代数余可裂正合序列,那么作为Hopf代数,由此有强增广余代数C的结构定理(作为双代数);如果为Hopf代数可裂正合序列,那么作为Hopf代数并简单地讨论了C×αH的余半单性. 相似文献
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利用Galois理论,研究了4次根式扩张的一些性质.利用这些性质,给出了域扩张是4次根式扩张的一些等价条件,证明了域扩张是4次根式扩张当且仅当域扩张是4次Galois扩张且Galois群是4阶循环群. 相似文献
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本文研究了弱Hopf-Galois扩张的扩张模.利用忠实平坦的弱Hopf-Galois扩张理论,研究了弱Hopf代数上的Militaru-Stefan提升定理,推广了文献[10]中的相应结果.进一步地,通过诱导模的自同态环的cleft扩张刻画了弱稳定模. 相似文献
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Adriana Balan 《代数通讯》2013,41(4):1491-1525
In this article, we consider categories of all semimodules over semirings which are p-Schreier varieties, i.e., varieties whose projective algebras are all free. Among other results, we show that over a division semiring R all semimodules are projective iff R is a division ring, prove that categories of all semimodules over proper additively π-regular semirings are not p-Schreier varieties (in particular, this result solves Problem 1 of Katsov [8]), as well as prove that categories of all semimodules over cancellative division semirings are, in contrast, p-Schreier varieties. 相似文献
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Žikica Perović 《Order》1998,15(3):199-202
We characterize Galois extensions of Boolean algebras as finite extensions with the independent set of generators, answering a question of D. Monk. 相似文献
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Xiao-Li Fang 《代数通讯》2013,41(7):2573-2597
Abstract We use the classification of finite order automorphisms by Kac to characterize all maximal subalgebras, regular, semisimple, reductive or not of a simple complex Lie algebra (up to conjugacy) that we can determine from its Dynkin diagram. Using Barnea et al. [Barnea, Y., Shalev, A., Zelmanov, E. I. (1998). Graded subalgebras of affine Kac–Moody algebras. Israel J. Math. 104:321–334] we extend our results to the case of affine Kac–Moody algebras. We also point out some inaccuracies in the Dynkin paper [Dynkin, E. B. (1957a). Semisimple subalgebras of semisimple Lie algebras. Amer. Math. Soc. Transl t. 6:111–244]. 相似文献
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Adriana Balan 《代数通讯》2013,41(4):1129-1150
If H is a finite dimensional quasi-Hopf algebra and A is a left H-module algebra, we show that there is a Morita context connecting the smash product A#H and the subalgebra of invariants A H . We define also Galois extensions and prove the connection with this Morita context, as in the Hopf case. 相似文献
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Min Ouyang 《Algebra Colloquium》2000,7(1):43-57
For H a finite-dimensional Hopf algebra over a field k, we study H*-Galois Azumaya extensions A, i.e., A is an H-module algebra which is H*-Galois with A/AH separable and AH Azumaya. We prove that there is a Galois correspondence between a set of separable subalgebras of A and a set of separable subalgebras of CA(AH), thus generalizing the work of Alfaro and Szeto for H a group algebra. We also study Galois bases and Hirata systems.1991 Mathematics Subject Classification: 16W30, 16H05 相似文献
16.
《代数通讯》2013,41(9):3437-3457
Abstract The notions of group coalgebra Galois extension and group entwining structure are defined. It is proved that any group coalgebra Galois extension induces a unique group-entwining map ψ = {ψα, β}α, β∈π compatible with the right group coaction, generalizing the recent work of Brzeziński and Hajac [Brzeziński, T., Hajac, P. M. (1999). Coalgebra extensions and algebra coextensions of Galois type. Comm. Algebra 27:1347–1368]. 相似文献
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Jos′e Nicanor Alonso ′ALVAREZ Jos′e Manue Fern′andez VILABOA Ram′on Gonz′alez RODR′IGUEZ 《数学年刊B辑(英文版)》2014,35(2):161-190
The authors present the general theory of cleft extensions for a cocommutative weak Hopf algebra H.For a right H-comodule algebra,they obtain a bijective correspondence between the isomorphisms classes of H-cleft extensions AH → A,where AH is the subalgebra of coinvariants,and the equivalence classes of crossed systems for H over AH.Finally,they establish a bijection between the set of equivalence classes of crossed systems with a fixed weak H-module algebra structure and the second cohomology group HφZ(AH)2(H,Z(AH)),where Z(AH)is the center of AH. 相似文献
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Let B be a ring with 1, C the center of B, G a finite automorphism group of B, and Ii = {c - gi(c) | c C} for each gi G. Then, B is called a center Galois extension with Galois group G if BIi = B for each gi 1 in G, and a weak center Galois extension with group G if BIi = Bei for some nonzero idempotent ei in C for each gi 1 in G. When ei is a minimal element in the Boolean algebra generated by {ei | gi G} Bei is a center Galois extension with Galois group Hi for some subgroup Hi of G. Moreover, the central Galois algebra B(1 – ei) is characterized when B is a Galois algebra with Galois group G.AMS Subject Classification (1991): 16S35 16W20Supported by a Caterpillar Fellowship, Bradley University, Peoria, Illinois, USA. We would like to thank Caterpillar Inc. for their support. 相似文献
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Weak coalgebra-Galois extensions are studied. A notion of an invertible weak entwining structure is introduced. It is proven that, within an invertible weak entwining structure, the surjectivity of the canonical map implies bijectivity, provided the structure coalgebra C is either coseparable or projective as a C-comodule. 相似文献