Classification of three-dimensional anti-dendriform algebras
Rings and Algebras
2024-04-02 v1
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.
Keywords
Cite
@article{arxiv.2404.00981,
title = {Classification of three-dimensional anti-dendriform algebras},
author = {K. Abdurasulov and J. Adashev and Z. Normatov and Sh. Solijonova},
journal= {arXiv preprint arXiv:2404.00981},
year = {2024}
}
Comments
14 pages. arXiv admin note: text overlap with arXiv:2209.08962 by other authors