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Radicals of PID's and Dedekind Domains

Published online by Cambridge University Press:  20 November 2018

R. E. Propes
R. E. Propes*
Affiliation:
The University of Wisconsin-Milwaukee, Milwaukee, Wisconsin
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The purpose of this paper is to characterize the radical ideals of principal ideal domains and Dedekind domains. We show that if T is a radical class and R is a PID, then T(R) is an intersection of prime ideals of R. More specifically, if

then T(R) = (p1p2 … pk), where p1, p2, … , pk are distinct primes, and where (p1p2 … Pk) denotes the principal ideal of R generated by p1p2 … pk. We also characterize the radical ideals of commutative principal ideal rings. For radical ideals of Dedekind domains we obtain a characterization similar to the one given for PID's.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 4 , August 1972 , pp. 566 - 572
Copyright
Copyright © Canadian Mathematical Society 1972

References

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