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arXiv · 2509.17090

Jordan homomorphisms of triangular algebras over noncommutative algebras

Oksana Bezushchak
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Abstract

D. Benkovi\v{c} 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 $\Phi$. Consider the algebra $T_n(R)$ of triangular $n \times n$ matrices over $R$, and its subalgebra $T_n^0(R)$ consisting of matrices whose main diagonal entries lie in $\Phi$. We prove that for any Jordan homomorphism of $T_n(R)$, its restriction to $T_n^0(R)$ is standard.

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Oksana Bezushchak. 2025-09-21. Jordan homomorphisms of triangular algebras over noncommutative algebras. https://arxiv.org/abs/2509.17090

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