Turkish Journal of Mathematics
DOI
-
Abstract
We investigate the relations between a radical submodule N of a module M being a finite intersection of prime submodules of M and the factor module M/N having finite uniform dimension. It is proved that if N is a radical submodule of a module M over a ring R such that M/N has finite uniform dimension, then N is a finite intersection of prime submodules. The converse is false in general but is true if the ring R is fully left bounded left Goldie and the module M is finitely generated. It is further proved that, in general, if a submodule N of a module M is a finite intersection of prime submodules, then the module M/N can have an infinite number of minimal prime submodules.
First Page
255
Last Page
270
Recommended Citation
SMITH, PATRICK F. (2004) "Radical Submodules and Uniform Dimension of Modules," Turkish Journal of Mathematics: Vol. 28: No. 3, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol28/iss3/4
