Jordan homomorphisms of triangular algebras over noncommutative algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918145065746432 |
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| author | Bezushchak, Oksana |
| author_facet | Bezushchak, Oksana |
| contents | 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 $n \times n$ matrices over $R$, and its subalgebra $T_n^0(R)$ consisting of matrices whose main diagonal entries lie in $Φ$. We prove that for any Jordan homomorphism of $T_n(R)$, its restriction to $T_n^0(R)$ is standard. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jordan homomorphisms of triangular algebras over noncommutative algebras Bezushchak, Oksana Rings and Algebras 16W10 (Primary) 15A30, 17C50 (Secondary) 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 $n \times n$ matrices over $R$, and its subalgebra $T_n^0(R)$ consisting of matrices whose main diagonal entries lie in $Φ$. We prove that for any Jordan homomorphism of $T_n(R)$, its restriction to $T_n^0(R)$ is standard. |
| title | Jordan homomorphisms of triangular algebras over noncommutative algebras |
| topic | Rings and Algebras 16W10 (Primary) 15A30, 17C50 (Secondary) |
| url | https://arxiv.org/abs/2509.17090 |