In this paper we prove the lying over and going down theorems for modules. Finally, we apply the above theorems and prove some results on the dimension of a module and its submodule.
KARIMZADEH, S. and NEKOOEI, REZA (2007) "On Dimension of Modules," Turkish Journal of Mathematics: Vol. 31: No. 1, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol31/iss1/8