On local finiteness in varieties of associative algebras

A variety $\mathfrak M$ of algebras is called distinguished if there is a countably generated, locally finite algebra $R\in\mathfrak M$ such that any other countably generated locally finite algebra $A\in\mathfrak M$ is a homomorphic image of $R$. This article continues the investigation of the question of when a variety of associative algebras is distinguished.
For example, if the ground field $\Phi$ is uncountable, then every distinguished variety is nonmatric. Note that nonmatric varieties over an algebraically closed field are always distinguished and, over a field $\Phi$ of characteristic zero, a nonmatric variety is distinguished if and only if $\dim_\Phi\widehat\Phi\leqslant\aleph_0$, where $\widehat\Phi$ is the algebraic closure of $\Phi$.
Bibliography: 16 titles.