ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS-Reference-Cited by-同舟云学术

ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS

Published:2013-12 Issue:08 Volume:23 Page:1881-1894
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

LOPATIN ARTEM A.¹,SHESTAKOV IVAN P.²

Affiliation:

1. Omsk Branch of Federal State Budgetary Scientific Establishment, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, (OB IM SBRAS), Pevtsova Street, 13, 644043, Omsk, Russia

2. Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010-Cidade Universitária, São Paulo-SP, CEP 05508-090, Brazil

Abstract

We study the nilpotency degree of a relatively free finitely generated associative algebra with the identity xn = 0 over a finite field 𝔽 with q elements. In the case of q ≥ n the nilpotency degree is proven to be the same as in the case of an infinite field of the same characteristic. In the case of q = n - 1 it is shown that the nilpotency degree differs from the nilpotency degree for an infinite field of the same characteristic by at most one. The nilpotency degree is explicitly computed for n = 3.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196713500471

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