Multiplication modules and a theorem of P. F. Smith

Majid M. Ali; David J. Smith

doi:10.1023/A:1019680010738

Multiplication modules and a theorem of P. F. Smith

Majid M. Ali^*, David J. Smith

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith's theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules.

Original language	English
Pages (from-to)	127-135
Number of pages	9
Journal	Periodica Mathematica Hungarica
Volume	44
Issue number	2
DOIs	https://doi.org/10.1023/A:1019680010738
Publication status	Published - 2002
Externally published	Yes

Keywords

Multiplication ideal
Multiplication module

ASJC Scopus subject areas

Mathematics(all)

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10.1023/A:1019680010738

Cite this

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abstract = "P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith's theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules.",

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AB - P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith's theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules.

KW - Multiplication ideal

KW - Multiplication module

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ER -

Multiplication modules and a theorem of P. F. Smith

Abstract

Keywords

ASJC Scopus subject areas

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