Let R be an associative ring with identity. A unital right R-module M is called "strongly finite dimensional" if Sup{G.dim(M/N)vertical bar N <= M}<+infinity, where G. dim denotes the Goldie dimension of a module. Properties of strongly finite dimensional modules are explored. It is also proved that: ( 1) If R is left F-injective and semilocal, then R is left finite dimensional. (2) R is right artinian if and only if R is right strongly finite dimensional and right semiartinian. Some known results are obtained as corollaries.
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