共查询到20条相似文献,搜索用时 31 毫秒
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ABSTRACT The role played by fields in relation to Galois Rings corresponds to semifields if the associativity is dropped, that is, if we consider Generalized Galois Rings instead of (associative) Galois rings. If S is a Galois ring and pS is the set of zero divisors in S, S* = S\ pS is known to be a finite {multiplicative} Abelian group that is cyclic if, and only if, S is a finite field, or S = ?/n? with n = 4 or n = p r for some odd prime p. Without associativity, S* is not a group, but a loop. The question of when this loop can be generated by a single element is addressed in this article. 相似文献
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Qi Xia 《高校应用数学学报(英文版)》2010,25(1):117-126
In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and K p algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of K p algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul algebra or to be a quasi-K p algebra. 相似文献
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《代数通讯》2013,41(5):1357-1368
Abstract The paper generalizes some of our previous results on quasi-hereditary Koszul algebras to graded standardly stratified Koszul algebras. The main result states that the class of standardly stratified algebras for which the left standard modules as well as the right proper standard modules possess a linear projective resolution – the so called linearly stratified algebras – is closed under forming their Yoneda extension algebras. This is proved using the technique of Hilbert and Poincaré series of the corresponding modules. 相似文献
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The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. 𝒦2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a 𝒦2 algebra would be another 𝒦2 algebra. We show that this is not necessarily the case by constructing a monomial 𝒦2 algebra for which the corresponding Yoneda algebra is not 𝒦2. 相似文献
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A diagram algebra in which the diagrams include n rows of n points is constructed. Moreover, we prove that the algebra is cellular and quasi-hereditary. 相似文献
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V. T. Filippov 《Mathematical Notes》1999,65(4):506-509
It is proved that ifS is a simple finite-dimensional anticommutative algebra over a field ϕ of characteristic zero satisfying the identityJ(x, y, z)t=J(t, z, xy)+J(t, y, zx)+J(t, x,yz), whereJ(x, y, z)=(xy)z+(zx)y+(yz)x, thenS is a Lie algebra.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 607–611, April, 1999. 相似文献
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A. P. Pojidaev 《代数通讯》2013,41(10):3593-3608
Derivations of the simple ternary Malcev algebra M 8 and its algebra of multiplications are described. 相似文献
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Antonio J. Calderón Martín 《代数通讯》2017,45(2):866-877
The class of extended Lie-type algebras contains the ones of associative algebras, Lie algebras, Leibniz algebras, dual Leibniz algebras, pre-Lie algebras, and Lie-type algebras, etc. We focus on the class of extended Lie-type algebras graded by an Abelian group G and study its structure, by stating, under certain conditions, a second Wedderburn-type theorem for this class of algebras. 相似文献
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V. Yu. Gubarev 《代数通讯》2013,41(2):497-520
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In this article, we describe all group gradings by a finite abelian group Γ of a simple Lie algebra of type G 2 over an algebraically closed field F of characteristic zero. 相似文献
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1 IntroductionVirasoro algebra and W algebra have been widely investigated by both physicists andmahematicians. Virasoro algebra can be thought of as the central extended algebra Of diffeOmorphisms Di$S') on the circle S1. In Ref[1], ftaPpat et al. extended the notion ofloop algebra g(S') to algebra g(M), M being a closed surface with dim M > 1, and gave thefolowing commutation relations:c,[Lk,l, L.,.] = [mp(k -- T) -- ftO(l -- 8)]Lk .,l , ti ll ghO(k -- j) -- fl0(l -- j)lok .,O8l ,,… 相似文献
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Jang-Ho Chun 《代数通讯》2013,41(10):3095-3102
For positive integers ? and n, several authors studied ??-gradings of the full matrix ring M n (k) over a field k. In this article, we show that every (G × H)-grading of M n (k) can be constructed by a pair of compatible G-grading and H-grading of M n (k), where G and H are any finite groups. When G and H are finite cyclic groups, we characterize all (G × H)-gradings which are isomorphic to a good grading. Moreover, the results can be generalized for any finite abelian group grading of M n (k). 相似文献
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It is proved that, for any metabelian Mal'tsev algebra M over a field of characteristic 2,3, there is an alternative algebra A such that the algebra M can be embedded in the commutator algebra A(-). Moreover, the enveloping alternative algebra A can be found in the variety of algebras with the identity [x,y][z,t] = 0. The proof of this result is based on the construction of additive bases of the free metabelian Mal'tsev algebra and the free alternative algebra with the identity [x,y][z,t] = 0. 相似文献
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Piotr Jędrzejewicz 《Central European Journal of Mathematics》2008,6(1):13-24
Let k be a field, let be a finite group. We describe linear -gradings of the polynomial algebra k[x
1, ..., x
m
] such that the unit component is a polynomial k-algebra.
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Gianfranco Casnati 《代数通讯》2013,41(8):2738-2761
Let k be an algebraically closed field of characteristic 0. We give here a complete classification of local commutative, associative, Artinian, Gorenstein k-algebras with unit, up to multiplicity 9. 相似文献