Primary modules over commutative rings

Smith, P.F. (2001) Primary modules over commutative rings. Glasgow Mathematical Journal, 43(1), pp. 103-111.

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Smith, Professor Patrick
Authors: Smith, P.F.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Glasgow Mathematical Journal
Publisher:Cambridge University Press
ISSN (Online):1469-509X
Published Online:04 June 2001
Copyright Holders:Copyright © 2001 Glasgow Mathematical Journal Trust
First Published:First published in Glasgow Mathematical Journal 43(1):103-111
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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