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Classification of multiplication modules over multiplication rings with finitely many minimal primes

Part of: Arithmetic rings and other special rings Theory of modules and ideals Chain conditions, finiteness conditions

Published online by Cambridge University Press:  03 October 2024

Volodymyr Bavula Open the ORCID record for Volodymyr Bavula [Opens in a new window]
Volodymyr Bavula*
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield, S3 7RH, UK
*
Email: [email protected]
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Abstract

A classification of multiplication modules over multiplication rings with finitely many minimal primes is obtained. A characterization of multiplication rings with finitely many minimal primes is given via faithful, Noetherian, distributive modules. It is proven that for a multiplication ring with finitely many minimal primes every faithful, Noetherian, distributive module is a faithful multiplication module, and vice versa.

Keywords

multiplication modulemultiplication ringDedekind domainArtinian local principal ideal ring

MSC classification

Primary: 13C05: Structure, classification theorems 13E05: Noetherian rings and modules 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 13F10: Principal ideal rings
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 67 , Issue 1 , January 2025 , pp. 67 - 71
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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References

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