Jordan homomorphisms of triangular algebras over noncommutative algebras

2025/09/21 by Оксана Безущак, Bezushchak, Oksana · 1 citation
Computer Science · Mathematics · #16W10 (Primary) 15A30 #17C50 (Secondary) #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2509.17090

openalex publication_date 2025/09/21 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

D. Benkovič described Jordan homomorphisms of algebras of triangular matrices over a commutative unital ring without additive 2-torsion. We extend this result to the case of noncommutative rings and remove the assumption of additive torsion. Let R be an associative unital algebra over a commutative unital ring Φ. Consider the algebra T_n(R) of triangular n × n matrices over R, and its subalgebra T_n⁰(R) consisting of matrices whose main diagonal entries lie in Φ. We prove that for any Jordan homomorphism of T_n(R), its restriction to T_n⁰(R) is standard.

Citations

• Jordan homomorphisms and T-ideals
• On Lie isomorphisms of rings

Cited by

• Jordan homomorphisms: A survey

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