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Primary and coprimary decompositions

Published online by Cambridge University Press:  20 January 2009

D. J. Moore
D. J. Moore
Affiliation:
University of Glasgow, Scotland
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Let R be an associative, commutative ring with identity, and let A be a (unitary) R-module. It is well known that if A is a Noetherian R-module then every submodule of A has a primary decomposition in A. The object of the present paper is to dualise this result; that is, to show that if A is an Artinian R-module then every submodule of A can be expressed as the sum of a finite number of coprimary submodules of A.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 4 , December 1973 , pp. 251 - 264
Copyright
Copyright © Edinburgh Mathematical Society 1973

References

REFERENCES

(1) Gabriel, P., Des Catégories Abéliennes, Bull. Soc. Math. France, 90 (1962), 323–448.CrossRefGoogle Scholar
(2) Matlis, E., Modules with Descending Chain Condition, Trans. Amer. Math. Soc. 97 (1960), 495–508.CrossRefGoogle Scholar
(3) Moore, D. J., 'Some Remarks on if-Sequences and R-Cosequences, J. London Math. Soc. (to appear).Google Scholar
(4) Northcott, D. G., Lessons on Rings, Modules and Multiplicities (Cambridge University Press, 1968).CrossRefGoogle Scholar