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Some Classes of Nilpotent Associative Algebras

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Abstract

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 \(C({\mathcal {A}})=(n-2,1,1)\) or \(C({\mathcal {A}})=(n-2,2)\).

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Acknowledgements

We thank the referee for the helpful comments and suggestions that contributed to improving this paper.

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Authors and Affiliations

  1. Andijan State University, Andijan, Uzbekistan

    I. A. Karimjanov

  2. Department of Mathematics, Institute of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain

    I. A. Karimjanov & M. Ladra

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  1. I. A. Karimjanov
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  2. M. Ladra
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Correspondence to M. Ladra.

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This work was supported by Agencia Estatal de Investigación (Spain), Grant MTM2016-79661-P and by Xunta de Galicia, Grant ED431C 2019/10 (European FEDER support included, UE).

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Karimjanov, I.A., Ladra, M. Some Classes of Nilpotent Associative Algebras. Mediterr. J. Math. 17, 70 (2020). https://doi.org/10.1007/s00009-020-1504-x

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  • DOI: https://doi.org/10.1007/s00009-020-1504-x

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