Ibn Al-Haitham Journal for Pure and Applied Sciences (May 2017)

On Fully Semiprime Submodules and Fully Semiprime Modules

  • I.M.A. Hadi,
  • B.N. Shihab

Journal volume & issue
Vol. 24, no. 2

Abstract

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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 XXW for all fully invariant R-submodule X of M, implies XW. 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.

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