@article { author = {Naghipour, A.R.}, title = {GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES}, journal = {Journal of Algebraic Systems}, volume = {3}, number = {1}, pages = {23-30}, year = {2015}, publisher = {Shahrood University of Technology}, issn = {2345-5128}, eissn = {2345-511X}, doi = {10.22044/jas.2015.484}, 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}, url = {https://jas.shahroodut.ac.ir/article_484.html}, eprint = {https://jas.shahroodut.ac.ir/article_484_b8aa3a43cefa546233e3447390d3917d.pdf} }