Primary modules over commutative rings

Patrick F. Smith

Type: Article

Publication Date: 2001-01-01

Citations: 42

DOI: https://doi.org/10.1017/s0017089501010084

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.

Locations

Glasgow Mathematical Journal - View - PDF
Enlighten: Publications (The University of Glasgow) - View - PDF

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Works Cited by This (5)

Action	Title	Year	Authors
+	Steps in commutative algebra	1991	Rodney Y. Sharp
+	On the prime radical of a module over a commutative ring	1992	James A. Jenkins Patrick F. Smith
+	Rings satisfying the radical formula	1996	Habib Sharif Yaghoub Sharifi Shohreh Namazi
+ PDF Chat	On commutative Noetherian rings which satisfy the radical formula	1997	Ka Hin Leung Shing Hing Man
+	Rings and Categories of Modules	1992	Frank W. Anderson Kent R. Fuller