Unit-regularity and representability for semiartinian -regular rings
We show that any semiartinian -regular ring is unit-regular; if, in addition, is subdirectly irreducible then it admits a representation within some inner product space.
We show that any semiartinian -regular ring is unit-regular; if, in addition, is subdirectly irreducible then it admits a representation within some inner product space.
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.