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Primary modules over commutative rings

Published online by Cambridge University Press:  04 June 2001

Patrick F. Smith
Patrick F. Smith
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, Scotland, UK e-mail:pfs@maths.gla.ac.uk
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The radical of a module over a commutative ring is the intersection of all prime submodules. It is proved that if R is a commutative domain which is either Noetherian or a UFD then R is one-dimensional if and only if every (finitely generated) primary R-module has prime radical, and this holds precisely when every (finitely generated) R-module satisfies the radical formula for primary submodules.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 1 , January 2001 , pp. 103 - 111
Copyright
2001 Glasgow Mathematical Journal Trust