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Polynomials determining Dedekind domains

Published online by Cambridge University Press:  17 April 2009

Jonathan A. Hillman
Jonathan A. Hillman
Affiliation:
Department of Mathematics, The Faculties, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.
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If A is a Dedekind domain and f generates a prime ideal of A[X] which is not maximal, then the domain A[X]/(f) is Dedekind if and only if f is not contained in the square of any maximal ideal of A[X]. This criterion is used find the ring of integers of a cyclotomic field, and to determine when a plane curve is normal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 2 , April 1984 , pp. 167 - 175
Copyright
Copyright © Australian Mathematical Society 1984

References

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