Let R be a right GF -closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorenstein ring R, the G...

Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated R-modules. For any n 0, we prove that R is a Gorenstein ring with self-injective dimension at most n if and only if every finitely generated left R-module and every finitely generated right R-module have torsionfree dimension at most n, if and only if every finitely generated le...

Let Λ be a left and right Artin ring and ΛωΛ a faithfully balanced selforthogonal bimodule. We give a sufficient condition that the injective dimension of ωΛ is finite implies that of Λω is also finite.  2003 Elsevier Science (USA). All rights reserved.

We give a characterization of right Noetherian semiprime semiperfect and semidistributive rings with inj. dimAAA 6 1.