共查询到20条相似文献,搜索用时 31 毫秒
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Cristina Draper Antonio Fernández López Esther García Miguel Gómez Lozano 《Journal of Algebra》2008,319(6):2372-2394
We define the socle of a nondegenerate Lie algebra as the sum of all its minimal inner ideals. The socle turns out to be an ideal which is a direct sum of simple ideals, and satisfies the descending chain condition on principal inner ideals. Every classical finite dimensional Lie algebra coincides with its socle, while relevant examples of infinite dimensional Lie algebras with nonzero socle are the simple finitary Lie algebras and the classical Banach Lie algebras of compact operators on an infinite dimensional Hilbert space. This notion of socle for Lie algebras is compatible with the previous ones for associative algebras and Jordan systems. We conclude with a structure theorem for simple nondegenerate Lie algebras containing abelian minimal inner ideals, and as a consequence we obtain that a simple Lie algebra over an algebraically closed field of characteristic 0 is finitary if and only if it is nondegenerate and contains a rank-one element. 相似文献
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Markku Niemenmaa 《Monatshefte für Mathematik》1986,101(3):183-191
We say that a near-ring (N,+,·) has an almost trivial multiplication (ATM) if the product of two elements belongs to the intersection of the additive cyclic groups generated by these two elements. We show that every finite near-ring with ATM can be decomposed to a direct sum where the summands are either near-rings defined on cyclic groups or near-rings whose minimal ideals are zero near-rings. Finally, we show how to construct these summands on cyclic groups. 相似文献
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We define the socle of an n-Lie algebra as the sum of all the minimal ideals. An n-Lie algebra is called metric if it is endowed with an invariant nondegenerate symmetric bilinear form. We characterize the socle of a metric n-Lie algebra, which is closely related to the radical and the center of the metric n-Lie algebra. In particular, the socle of a metric n-Lie algebra is reductive, and a metric n-Lie algebra is solvable if and only if the socle coincides with its center. We also calculate the metric dimensions of simple and reductive n-Lie algebras and give a lower bound in the nonreductive case. 相似文献
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We show that minimal ideals of Jordan systems (algebras, triple systems, and pairs) are either simple or trivial, so answering
the question posed by Nam and McCrimmon in 1983.
Mathematics Subject Classification (2000) 17C10, 17C20 相似文献
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Antonio Fernández López 《代数通讯》2017,45(4):1577-1583
In a recent paper by the author and Golubkov, it was proved that a strongly prime Lie PI-algebra with an algebraic adjoint representation over an algebraically closed field of characteristic 0 is simple and finite dimensional. In this note, we derive this result from a more general one on strongly prime Lie PI-algebras with abelian minimal inner ideals, which is closely related to the intrinsic characterization of simple finitary Lie algebras with abelian minimal inner ideals. 相似文献
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E. Momtahan 《代数通讯》2013,41(12):4739-4746
In this article, we study essential ideals, socle, and some related ideals of rings of real valued measurable functions. We also study the Goldie dimension of rings of measurable functions. 相似文献
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We introduce some determinantal ideals of the generalized Laplacian matrix associated to a digraph G, that we call critical ideals of G. Critical ideals generalize the critical group and the characteristic polynomials of the adjacency and Laplacian matrices of a digraph. The main results of this article are the determination of some minimal generator sets and the reduced Gröbner basis for the critical ideals of the complete graphs, the cycles and the paths. Also, we establish a bound between the number of trivial critical ideals and the stability and clique numbers of a graph. 相似文献
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Shmuel Glasner 《Israel Journal of Mathematics》1975,22(1):87-92
We show that a minimal metric flowX whose enveloping semigroupE(X), contains finitely many minimal ideals, is a PI-flow; i.e.X has a proximal extensionX' which can be built by iterating proximal and isometric extensions (starting with the trivial one point flow). An example is given which shows that the converse theorem does not hold. Finally, we show that ifX is a minimal, non-trivial, metric, weakly mixing flow and the group action is nilpotent thenE(X) contains infinitely many minimal ideals. 相似文献
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The Kumjian–Pask algebra KP(Λ) is a graded algebra associated to a higher-rank graph Λ and is a generalization of the Leavitt path algebra of a directed graph. We analyze the minimal left ideals of KP(Λ), and identify its socle as a graded ideal by describing its generators in terms of a subset of vertices of the graph. We characterize when KP(Λ) is semisimple, and obtain a complete structure theorem for a semisimple Kumjian–Pask algebra. As a consequence of this structure theorem, every semisimple Kumjian–Pask algebra can be obtained as a Leavitt path algebra of a directed graph. 相似文献
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E. P. Vdovin 《Proceedings of the Steklov Institute of Mathematics》2014,285(1):183-190
It is proved that, if a Hall subgroup of an almost simple group whose socle is an exceptional group of Lie type is solvable, then there exist four groups conjugate to it whose intersection is trivial. 相似文献
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David Bachiller 《Journal of Pure and Applied Algebra》2018,222(7):1670-1691
We show how to construct all the extensions of left braces by ideals with trivial structure. This is useful to find new examples of left braces. But, to do so, we must know the basic blocks for extensions: the left braces with no ideals besides the trivial and the total ideal, called simple left braces. In this article, we present the first non-trivial examples of finite simple left braces. To explicitly construct them, we define the matched product of two left braces, which is a useful method to recover a finite left brace from its Sylow subgroups. 相似文献
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The algebra of m×m matrices over real numbers, complex numbers or quaternions is equipped with the standard inner product Re tr(xy *) Work done in part during the Summer Research Institute of the Canadian Mathematical Congress, 1971.). It is easy to see that the left ideals of this algebra have the property that the projections of unitary matrices on them have constant length. of course, the right ideals have the same property. This property and a condition on dimension give a characterization of minimal left or right ideals of this algebra. We use this characterization to determine all orthogonal transformations of this algebra which preserve unitary matrices. 相似文献
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Ali Akbar Mehrvarz Kamal Bahmanpour Reza Naghipour 《Algebras and Representation Theory》2014,17(4):1207-1215
The purpose of this paper is to give some equivalent conditions to the socle and Bass numbers’ conjectures which raised by Huneke in (Res Notes Math 2:93–108,). In addition, some results about certain Gorenstein ideals are included. 相似文献