Abstract
This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. 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 nonzero idempotent element is nilpotent. If an associative algebra has a nonzero idempotent element, then there does not exist a compatible anti-dendriform algebra structure associated with associative algebras.
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