The Lie Inner Ideal Structure of Associative Rings Revisited

DOI10.1080/00927870802545729zbMath1210.16038OpenAlexW2006405387MaRDI QIDQ3653325

Antonio Fernández López, Georgia M. Benkart

Publication date: 22 December 2009

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927870802545729

zbMATH Keywords

idempotentsskew-symmetric elementsJordan pairsminimal one-sided idealssimple rings with involutioncentral simple Lie algebrasLie inner ideals

Mathematics Subject Classification ID

Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Jordan structures associated with other structures (17C50) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Ideals in associative algebras (16D25) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items (9)

Abelian Non Jordan-Lie Inner Ideals of the Orthogonal Finite Dimensional Lie Algebras ⋮ Generalization of Jordan-Lie inner ideals of finite dimensional associative algebras ⋮ Развитие понятия «артиновость» для алгебр Ли ⋮ A filtration associated to an abelian inner ideal of a Lie algebra ⋮ On a class of finitary Lie algebras characterized through derivations ⋮ Inner ideals of Lie algebras of skew elements of prime rings with involution ⋮ Jordan-Lie inner ideals of finite dimensional associative algebras ⋮ Maximal zero product subrings and inner ideals of simple rings ⋮ Inner ideals of real simple Lie algebras

Cites Work

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• Simple Lie algebras having extremal elements
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• Simple associative algebras with finite \(\mathbb{Z}\)-grading
• The Jordan socle and finitary Lie algebras
• On the geometry of inner ideals
• The socle of a nondegenerate Lie algebra
• An Artinian theory for Lie algebras
• LIE ALGEBRAS WITH A FINITE GRADING
• Jordan pairs with finite grids

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