Associative nil-algebras over finite fields

Artem A. Lopatin; Ivan P. Shestakov

arXiv:1303.0898·math.RA·March 6, 2013·Int. J. Algebra Comput.

Associative nil-algebras over finite fields

Artem A. Lopatin, Ivan P. Shestakov

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TL;DR

This paper investigates the nilpotency degree of relatively free finitely generated associative algebras with the identity x^n=0 over finite fields, providing insights into their algebraic structure.

Contribution

It offers new results on the nilpotency degree of these algebras over finite fields, expanding understanding of their properties.

Findings

01

Determined the nilpotency degree for specific cases

02

Established bounds for the nilpotency degree over finite fields

03

Compared properties over different finite fields

Abstract

The nilpotency degree of a relatively free finitely generated associative algebra with the identity $x^{n} = 0$ is studied over finite fields.

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