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.
|Number of pages||9|
|Journal||Periodica Mathematica Hungarica|
|Publication status||Published - 2002|
- Multiplication ideal
- Multiplication module
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