Some classes of nilpotent associative algebras
Ikboljon A. Karimjanov, Manuel Ladra

TL;DR
This paper classifies specific types of nilpotent associative algebras, including filiform and quasi-filiform algebras, over fields of characteristic zero, providing a detailed structural understanding.
Contribution
It offers a comprehensive classification of filiform and naturally graded nilpotent associative algebras with particular characteristic sequences, expanding the understanding of their structure.
Findings
Classification of filiform associative algebras of degree k
Classification of naturally graded complex filiform and quasi-filiform nilpotent associative algebras
Descriptions based on characteristic sequences C(A)=(n-2,1,1) and C(A)=(n-2,2)
Abstract
In this paper we classify filiform associative algebras of degree over a field of characteristic zero. Moreover, we also classify naturally graded complex filiform and quasi-filiform nilpotent associative algebras which are described by the characteristic sequence or .
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