Local and 2-local automorphisms of null-filiform and filiform associative algebras

In the present paper automorphisms, local and 2-local automorphisms of $n$-dimensional null-filiform and filiform associative algebras are studied. Namely, a common form of the matrix of automorphisms and local automorphisms of these algebras is clarified. It turns out that the common form of the matrix of an automorphism on these algebras does not coincide with the local automorphism's matrices common form on these algebras. Therefore, these associative algebras have local automorphisms that are not automorphisms.Also, that each 2-local automorphism of null-filiform algebra is an automorphism and some associative filiform algebras admit 2-localautomorphisms which are not automorphisms are proved. This work was partially supported by RSF 22-71-10001