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February 8, 2026Journal of the London Mathematical SocietyOpen Access

Jordan homomorphisms and T‐ideals

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Authors

MBMatej BrešarUniversity of LjubljanaEZEfim ZelmanovSouthern University of Science and Technology

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Implication

This research demonstrates extensions of Jordan homomorphisms in algebras with trivial annihilator, highlighting limitations.

Key Points

  • The aim is to investigate the conditions under which Jordan homomorphisms can be expressed as sums of homomorphisms and antihomomorphisms.
  • Analyzed associative algebras with a focus on commutator ideals.
  • Examined properties of Jordan homomorphisms under specific ideal conditions.
  • Identified a counter-example regarding trivial annihilator assumptions.
  • Every Jordan epimorphism can be decomposed into a homomorphism and an antihomomorphism.
  • Existence of an ideal that allows extension of a Jordan homomorphism to an associative homomorphism under certain conditions.
  • Elements of the ideal of identities in matrix algebras are nilpotent modulo the examined ideal.

Cite This Study

Brešar et al. (2026) studied this question.

synapsesocial.com/papers/698827a20fc35cd7a884678dhttps://doi.org/10.1112/jlms.70448
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