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Periodica Mathematica Hungarica
Volume/Issue:
Volume 18: Issue 4
DOI:
https://doi.org/10.1007/bf01848103
Author:
A. Naoum
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Periodica Mathematica Hungarica
Volume/Issue:
Volume 44: Issue 2
DOI:
https://doi.org/10.1023/a:1019680010738
Authors:
Majid Ali
and
David Smith

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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Periodica Mathematica Hungarica
Volume/Issue:
Volume 16: Issue 4
DOI:
https://doi.org/10.1007/bf01848075
Authors:
A. Naoum
and
M. Hasan
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