共查询到20条相似文献,搜索用时 0 毫秒
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Peter Brown 《代数通讯》2013,41(4):1005-1015
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Manuel Saorín 《Journal of Pure and Applied Algebra》2010,214(9):1553-1558
We show that if H is a hereditary finite dimensional algebra, M is a finitely generated H-module and B is a semisimple subalgebra of EndH(M)op, then the representation dimension of is less than or equal to 3 whenever one of the following conditions holds: (i) H is of finite representation type; (ii) H is tame and M is a direct sum of regular and preprojective modules; (iii) M has no self-extensions. 相似文献
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Karim Johannes Becher David B. Leep Claus Schubert 《Israel Journal of Mathematics》2014,199(2):547-566
We study the behavior of orderings, semiorderings, and the stability index under field extensions. 相似文献
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Julie Dionne 《Journal of Pure and Applied Algebra》2009,213(2):241-228
We show that the main results of Happel-Rickard-Schofield (1988) and Happel-Reiten-Smalø (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if G is a finite group acting on a piecewise hereditary algebra A over an algebraically closed field whose characteristic does not divide the order of G, then the resulting skew group algebra A[G] is also piecewise hereditary. 相似文献
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Claus Schubert 《Mathematische Zeitschrift》2011,269(1-2):137-146
For a field F of characteristic not 2, let ${\widehat{F}}$ denote the maximal dimension of anisotropic, weakly isotropic, non-degenerate quadratic forms over F. In this paper, we investigate the behavior of this invariant under field extensions. 相似文献
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Karim Johannes Becher Nicolas Grenier-Boley Jean-Pierre Tignol 《Archiv der Mathematik》2018,111(2):135-143
Two different proofs are given showing that a quaternion algebra Q defined over a quadratic étale extension K of a given field has a corestriction that is not a division algebra if and only if Q contains a quadratic algebra that is linearly disjoint from K. This is known in the case of a quadratic field extension in characteristic different from two. In the case where K is split, the statement recovers a well-known result on biquaternion algebras due to Albert and Draxl. 相似文献
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Cluster-tilted algebras as trivial extensions 总被引:1,自引:0,他引:1
Given a finite-dimensional algebra C (over an algebraicallyclosed field) of global dimension at most two, we define itsrelation-extension algebra to be the trivial extension C Ext(DC,C) of C by the C–C-bimoduleExt(DC,C). We give a constructionfor the quiver of the relation-extension algebra in case thequiver of C has no oriented cycles. Our main result says thatan algebra is cluster-tilted if and only if there exists a tilted algebra C such that is isomorphic to the relation-extensionof C. 相似文献
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《Journal of Pure and Applied Algebra》2021,225(12):106773
Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms of central simple graded-division algebras.On the other hand, given a finite abelian group G, any central simple G-graded-division algebra over a field is determined, thanks to a result of Picco and Platzeck, by its class in the (ordinary) Brauer group of and the isomorphism class of a G-Galois extension of .This connection is used to classify the simple G-Galois extensions of in terms of a Galois field extension with Galois group isomorphic to a quotient and an element in the quotient subject to certain conditions. Non-simple G-Galois extensions are induced from simple T-Galois extensions for a subgroup T of G. We also classify finite-dimensional G-graded-division algebras and, as an application, finite G-graded-division rings. 相似文献
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Karla Čipková 《Czechoslovak Mathematical Journal》2006,56(3):933-947
Let A and B be graph algebras. In this paper we present the notion of an ideal in a graph algebra and prove that an ideal extension of
A by B always exists. We describe (up to isomorphism) all such extensions. 相似文献