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A remark on the distributive law for an ideal in a commutative ring

Published online by Cambridge University Press:  18 May 2009

C. U. Jensen
C. U. Jensen
Affiliation:
University of Copenhagen
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Let R be a commutative ring, with an identity element. It is the purpose of this note to establish conditions for an arbitrary but fixed ideal a of R to satisfy the distributive law

for all ideals b and c of R. In particular, in the Noetherian case, this will be related to the decomposition of a into prime ideals. We start with

Proposition 1. For a fixed ideal a in a commutative ring R with an identity element, the following conditions are equivalent.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 4 , July 1966 , pp. 193 - 198
Copyright
Copyright © Glasgow Mathematical Journal Trust 1966

References

REFERENCES

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