Varieties and sums of rings.
Varieties of associative rings closed under ideal sums
Varieties with polynomially many models, I
A characterization of locally finite congruence modular varieties with the number of at most k-generated models being bounded from above by a polynomial in k is given. These are exactly the varieties polynomially equivalent to the varieties of unitary modules over a finite ring of finite representation type.
VNR rings, -regular rings and annihilators
Von Neumann regular rings, hereditary rings, semi-simple Artinian rings, self-injective regular rings are characterized. Rings which are either strongly regular or semi-simple Artinian are considered. Annihilator ideals and -regular rings are studied. Properties of WGP-injectivity are developed.
Von Neumann regular rings and the Whitehead property of modules