| Title: | Jordan homomorphisms and T-ideals |
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| Authors: | ID Brešar, Matej (Author)
ID Zelmanov, Efim (Author) |
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| Files: |  PDF - Presentation file, download (332,04 KB)
MD5: 1B134B7F607A2A4FD4F1A71086CCED4B
 URL - Source URL, visit https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70448
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | Let $A$ and $B$ be associative algebras over a field $F$ with ${\rm char}(F)\ne 2$. Our first main result states that if $A$ is unital and equal to its commutator ideal, then every Jordan epimorphism $\varphi:A\to B$ is the sum of a homomorphism and an antihomomorphism. Our second main result concerns (not necessarily surjective) Jordan homomorphisms from $H(A,*)$ to $B$, where $*$ is an involution on $A$ and $H(A,*)=\{a\in A\,|\, a^*=a\}$. We show that there exists a ${\rm T}$-ideal $G$ having the following two properties: (1) the Jordan homomorphism $\varphi:H(G(A),*)\to B$▫ can be extended to an (associative) homomorphism, subject to the condition that the subalgebra generated by $\varphi(H(A,*))$ has trivial annihilator, and (2) every element of the ${\rm T}$-ideal of identities of the algebra of $2\times 2$ matrices is nilpotent modulo $G$. A similar statement is true for Jordan homomorphisms from $A$ to $B$. A counter-example shows that the assumption on trivial annihilator cannot be removed. |
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| Keywords: | Jordan homomorphisms, trivial annihilator, T-ideals |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.02.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 24 str. |
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| Numbering: | Vol. 113, iss. 2, article no. e70448 |
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| PID: | 20.500.12556/DiRROS-28861  |
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| UDC: | 512 |
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| ISSN on article: | 0024-6107 |
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| DOI: | 10.1112/jlms.70448 |
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| COBISS.SI-ID: | 274702595 |
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| Note: |
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| Publication date in DiRROS: | 09.04.2026 |
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| Views: | 38 |
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| Downloads: | 18 |
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