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On the Ideal Equation I(B ∩ C) = IB∩IC

Published online by Cambridge University Press:  20 November 2018

D. D. Anderson
D. D. Anderson*
Affiliation:
The University of Iowa, Iowa City, Iowa 52242
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Abstract

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Let R be an integral domain with quotient field K and let I be a nonzero ideal of R. We show (1) that I is invertible if and only if for every nonempty collection {Bα} of ideals of R and (2) that I is flat if and only if I(B ∩ C) = IB∩IC for each pair of ideals B and C of R.

Keywords

13C1113G05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 331 - 332
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Bourbaki, N., Commutative Algebra, Addison-Wesley, Reading, Mass., 1972 Google Scholar
2. Gilmer, R., Multiplicative Ideal Theory, Marcel Dekker, New York, 1972.Google Scholar