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arXiv · 2404.00981

Classification of three-dimensional anti-dendriform algebras

K. Abdurasulov·J. Adashev·Z. Normatov·Sh. Solijonova
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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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BibTeXRIS

K. Abdurasulov, J. Adashev, Z. Normatov, Sh. Solijonova. 2024-04-01. Classification of three-dimensional anti-dendriform algebras. https://arxiv.org/abs/2404.00981

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