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On Fully Semiprime Submodules and Fully Semiprime Modules | ||
| Ibn Al-Haitham Journal For Pure And Applied Science | ||
| Article 1, Volume 24, Issue 2, 2011, Pages 300-309 | ||
| Authors | ||
| B.N. Shihab; | ||
| Abstract | ||
| Let R be a commutative ring with unity and let M be a unitary R-module. In this paper we study fully semiprime submodules and fully semiprime modules, where a proper fully invariant R-submodule W of M is called fully semiprime in M if whenever XXW for all fully invariant R-submodule X of M, implies XW. M is called fully semiprime if (0) is a fully semiprime submodule of M. We give basic properties of these concepts. Also we study the relationships between fully semiprime submodules (modules) and other related submodules (modules) respectively.Key words: Fully semiprime submodule, fully semiprime modules, fully invariant submodule, fully prime modules. | ||
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