Document Type: Research Note

Author

• A.R. Naghipour

Department of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iran.

Abstract

The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this
definition, we extend the Generalized Principal Ideal Theorem to modules.

Keywords

• Generalized Principal Ideal Theorem
• Prime submodule
• Completely prime submodule