Classification of three-dimensional anti-dendriform algebras

2024/04/01 by Kobiljon Abdurasulov, Abdurasulov, K., J. Q. Adashev +5 · 1 citation
Computer Science · Mathematics · #16P10 #17A30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2404.00981

openalex publication_date 2024/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. They are characterized as algebras with two operations whose sum is associative. In particular, the paper is devoted to classifying anti-dendriform algebras associated with null-filiform associative algebras and three-dimensional algebras. It is known that any finite-dimensional associative algebra without a non-zero idempotent element is nilpotent. If an associative algebra has a non-zero idempotent element, then there does not exist a compatible anti-dendriform algebra structure associated with associative algebras.

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