Title of article :
On radical formula and Prufer domains
Author/Authors :
Mirzaei ، F. - Shahid Bahonar University of Kerman , NEKOOEI ، R. - Shahid Bahonar University of Kerman
Abstract :
In this paper we characterize the radical of an arbitrary submodule N of a finitely generated free module F over a commutatitve ring R with identity. Also we study submodules of F which satisfy the radical formula. Finally we derive necessary and sufficient conditions for R to be a Pru¨fer domain, in terms of the radical of a cyclic submodule in R⨁R.
Keywords :
Prime submodules , Radical of a submodule , Radical formula , Prufer domains , Dedekind domains
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
