On radical formula and Prufer domains

Document Type : Research Paper


Department of Pure‎ ‎Mathematics‎, ‎Faculty of Mathematics and Computer, Shahid Bahonar‎ ‎University‎ ‎of Kerman‎, ‎P.O. Box 76169133, Kerman‎, ‎Iran.


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 ‎Pr$\ddot{\mbox{u}}$fer domain‎, ‎in terms of the radical of a‎ ‎cyclic submodule in $R\bigoplus R$‎.‎  


Main Subjects

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