Primary modules over commutative rings

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

Abstract

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
• Status: Published
• Refereed: Yes
• 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: 0017-0895
• 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