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Ideal Decompositions in Noetherian Rings

Published online by Cambridge University Press:  20 November 2018

Wilfred E. Barnes  and
William M. Cunnea
Wilfred E. Barnes
Affiliation:
Washington State University
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An interesting identity is obtained for ideals A and B in a Noetherian ring :

A = (A + Bn) ∩ (A : Bn)

for sufficiently large n. This identity is applied to obtain Fuchs' quasi-primary decomposition of A in an improved form, and to obtain Krull's theorem on the intersection of the powers of A, both developments making no use of the Noetherian primary decomposition of A. Finally, the identity is used to obtain the primary decomposition without reference to irreducible ideals, in a largely constructive manner which yields the decomposition in an illuminating, automatically normal form, and which, subject to certain simple conditions, is unique.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 178 - 184
Copyright
Copyright © Canadian Mathematical Society 1965

References

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