Jordan Rings with Nonzero Socle

DOI10.2307/1998700zbMath0409.17014OpenAlexW4252704784MaRDI QIDQ4196573

J. Marshall Osborn, Michel L. Racine

Publication date: 1979

Full work available at URL: https://doi.org/10.2307/1998700

zbMATH Keywords

Quadratic Jordan AlgebraMinimal Inner IdealPrime Jordan AlgebraPrimitive Associative RingSocle

Mathematics Subject Classification ID

Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Structure theory for Jordan algebras (17C10) Simple, semisimple Jordan algebras (17C20)

Related Items

Local orders in Jordan algebras, On the socle of a noncommutative Jordan algebra, Jordan canonical form for finite rank elements in Jordan algebras, The Jordan algebras of a Lie algebra, Algebra norms on tensor products of algebras, and the norm extension problem, Modulap annihilator jordan algebras, Spectral characterization of the socle in Jordan–Banach algebras, Prime Jordan P.I. algebras with nonzero socle and Jordan division algebras, Lie algebras with an algebraic adjoint representation revisited, Primitive Noncommutative Jordan Algebras with Nonzero Socle, Proc. Nat. Acad. Sei, Topological radicals, VI. Scattered elements in Banach Jordan and associative algebras, Unnamed Item, Goldie theory for Jordan algebras.

Cites Work

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• Peirce ideals in Jordan algebras
• Triality and Lie algebras of type \(D_4\)
• Lectures on quadratic Jordan algebras
• The structure of algebraic jordan algebras without nonzero nilpotent elements
• Speciality and reflexivity of quadratic jordan algebras
• Jordan Algebras with Interconnected Idempotents
• The Prime Radical in a Jordan Ring
• Inner Ideals in Quadratic Jordan Algebras
• The Freudenthal-Springer-Tits Constructions Revisited
• The Prime Radical in Special Jordan Rings
• Homomorphisms of Jordan Rings of Self-Adjoint Elements