20.500.12556/DiRROS-28861 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 Ni določen Neznano 2026-04-09 14:23:22 2026-04-09 14:23:22 2026-04-10 03:55:41 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 1B134B7F607A2A4FD4F1A71086CCED4B 9cca5f901724d37a3bdf44fbc2a64e74cf165964cd526166c72aa2b17c31083f fed982cd-340e-11f1-b941-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43018 https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70448 1 e8e6d870-340e-11f1-b941-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43017 Inštitut za matematiko, fiziko in mehaniko 0 0 0