Document Type: Research Note

Author

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