Geodesic
Radicals of PID's and Dedekind Domains
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 566-572

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Propes, R. E. Radicals of PID's and Dedekind Domains. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 566-572. doi: 10.4153/CJM-1972-050-2
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