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Abstract
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An R-module M is called semiprime (resp. weakly compressible) if every essential submod-
ule of MR cogenerates MR (resp. Hom_{R}(M;N)N\neq 0 for each 0 0\neq N M_R). Weakly
compressible modules are semiprime. We investigate when a semiprime module is weakly
compressible over any ring R. It is also shown that over the certain rings R, including right
duo rings and right FBN rings, every semiprime module with nite uniform dimension is
weakly compressible. These give a partial answer to an open problem in [6, Open problem
2, page 92].
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