20.500.12556/RUL-181514 Jordan homomorphisms and T-ideals 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. Jordan homomorphisms trivial annihilator T-ideals true false true Angleški jezik Angleški jezik Članek v reviji 2026-04-09 14:16:27 2026-04-09 14:16:31 2026-04-14 08:53:47 0000-00-00 00:00:00 2026 0 0 24 str. iss. 2, article no. e70448 Vol. 113 Feb. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-02-01 512 0024-6107 10.1112/jlms.70448 274702595 Journal_of_London_Math_Soc_-_2026_-_Bresar_-_Jordan_homomorphisms_and_T‐ideals.pdf Journal_of_London_Math_Soc_-_2026_-_Bresar_-_Jordan_homomorphisms_and_T‐ideals.pdf 1 F3C5BA3B5A8E8B62EF897A8C915E7BB1 18e069f32a68f50c98e4205f956b58444f3a18a52d1d12be7411981d2881f4ac 3831dcc2-340e-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=232043 https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70448 1 bf72a149-340d-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=232041 Fakulteta za matematiko in fiziko 0 0 0