Askar Dzhumadildaev2025-11-042025-11-042007Askar Dzhumadildaev / Quasi-Associative Algebras / Suleyman Demirel University / Сду хабаршысы, 2007https://repository.sdu.edu.kz/handle/123456789/2131This paper investigates a class of algebras obtained from associative algebras by introducing a q-commutator defined as a * b = ab + qba, where q belongs to a field K with characteristic not equal to 2 or 3, and q² is not equal to 0 or 1. Using this commutator, we construct algebras that form a variety characterized by a q-associativity identity. When the parameter satisfies q² − 4q + 1 ≠ 0, this identity alone describes the entire variety of q-associative algebras. However, when q² − 4q + 1 = 0, the q-associativity identity must be supplemented by the Lie-admissibility identity. In this exceptional case, the resulting variety is equivalent to the class of alternative algebras. Therefore, q-associative algebras form a structural link between associative, Lie-admissible, and alternative algebras, demonstrating how small changes in the commutator parameter q can transform fundamental algebraic properties.enAttribution-NonCommercial-ShareAlike 4.0 Internationalquasi-associative algebrasq-commutatoralgebraic identitiesassociatorsLie-admissible algebrasalternative algebrasArticle