TY - JOUR
T1 - Multiplication modules and a theorem of P. F. Smith
AU - Ali, Majid M.
AU - Smith, David J.
PY - 2002
Y1 - 2002
N2 - 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.
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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U2 - 10.1023/A:1019680010738
DO - 10.1023/A:1019680010738
M3 - Article
AN - SCOPUS:52649117592
SN - 0031-5303
VL - 44
SP - 127
EP - 135
JO - Periodica Mathematica Hungarica
JF - Periodica Mathematica Hungarica
IS - 2
ER -