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

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.