Critical vector spaces and extremal $L$-varieties

A. V. Kislitsin

Altai State Pedagogical University, Barnaul, Russia

Abstract: An example of an almost commutative, almost Engel and almost finitely based $L$-variety is presented that is generated by a multiplicative vector space distinct from its enveloping algebra. Also, an example of a critical multiplicative vector space is constructed that is not a linear algebra.

Keywords: almost $\theta$-variety, extremal variety, multiplicative vector space, multiplicative vector space identity, critical multiplicative vector space, $L$-variety.

MSC: 16R10

Received: 06.11.2024 and 10.04.2025

DOI: 10.4213/sm10232