Local and 2-local anti-derivations on filiform associative algebras

This paper is devoted to the study of local and 2-local anti-derivations of null-filiform, filiform and naturally graded quasi-filiform associative algebras. We prove that these algebras as a rule admit local anti-derivations which are not anti-derivations. We show that filiform and naturally graded quasi-filiform associative algebras admit 2-local anti-derivations which are not anti-derivations and any 2-local anti-derivation of null-filiform associative algebras is an anti-derivation.

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