This article is cited in 1 paper

Mathematical logic, algebra and number theory

On the standard identity in a finitely generated nilpotent algebra $R$ over an arbitrary field with condition $\dim R^{N}/R^{N+1} = 2$

E. P. Petrov

Altai State University, 61, Lenina ave., Barnaul, 656049, Russia

Abstract: In this paper it is proved that $s$-generated nilpotent algebra $R$ over arbitrary field with condition $\dim R^{N}/R^{N+1} = 2$ for some natural number $N \geq 3$ satisfies the standard identity of degree $N+2$ if $s\geq N$, or the standard identity of smaller degree than $N$ if $s < N$. The results of this article on a characteristic field other than 2 were obtained in a previous work by the author, published in SEMR.

Keywords: defining relations, identities, nilpotent algebra.

UDC: 512.552.4

MSC: 16R10

Received October 9, 2019, published December 26, 2019

DOI: 10.33048/semi.2019.16.142

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