on radical formula and prufer domains
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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 pr$ddot{mbox{u}}$fer domain, in terms of the radical of a cyclic submodule in $rbigoplus r$.
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Journal title:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۳، صفحات ۵۵۵-۵۶۳
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