On Strong Goldie Dimension

Abstract

Let R be an associative ring with identity. A unital right Rmodule M is called strongly finite dimensional if Sup{G.dim(M/N ) | N ≤ M } < +∞. Properties of strongly finite dimensional modules are explored. It is also proved that: (1)If R is left F -injective and strongly right finite dimensional, then R is left finite dimensional. (2) If R is right Finjective, then R is right finite dimensional if and only if R is semilocal. Thus the Faith-Menal conjecture is true if R is strongly right finite dimensional. Some known results are obtained as corollaries.