نجمه دهقانی

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].