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Abstract
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) | N ≤ M} < +∞, 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.
Mathematics Subject Classification:
ACKNOWLEDGMENTS
The authors gratefully thank the referee for his careful reading the article and giving many nice suggestions. The research was supported by the Foundation of Southeast University (No. 4007011034), the National Natural Science Foundation of China (No. 10571026), the National Natural Science Foundation of Jiangsu Province (No. BK2005207), and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutes of MOE, China.
Notes
Communicated by I. Swanson.