Varieties of associative rings containing a finite ring that is nonrepresentable by a matrix ring over a commutative ring (Q291231)

In this paper, infinite series of finite noncritical rings that are not representable by matrix rings over commutative rings are constructed. Moreover, the basis of polynomial identities of these rings is found. It is proved that every variety generated by one of these rings is a minimal variety containing a finite ring that is nonrepresentable by a matrix ring over a commutative ring. Finally, the author describes almost finitely representable varieties of rings generated by rings containing an idempotent of additive order \(p\), where \(p\) is a prime number.