Some Classes of Nilpotent Associative Algebras

@article{Karimjanov2020SomeCO,
  title={Some Classes of Nilpotent Associative Algebras},
  author={I. A. Karimjanov and Manuel Ladra},
  journal={Mediterranean Journal of Mathematics},
  year={2020},
  volume={17},
  pages={1-21}
}
In this paper, we classify filiform associative algebras of degree p over a field of characteristic zero. Moreover, over an algebraically closed field of characteristic zero, we also classify filiform nilpotent associative algebras and naturally graded quasi-filiform nilpotent associative algebras, described through the characteristic sequence $$C({\mathcal {A}})=(n-2,1,1)$$ C ( A ) = ( n - 2 , 1 , 1 ) or $$C({\mathcal {A}})=(n-2,2)$$ C ( A ) = ( n - 2 , 2 ) . 
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