Vol. 86, No. 2, 1980

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A note on tamely ramified polynomials

Joe Peter Buhler

Vol. 86 (1980), No. 2, 421–425

Let f(x) be a monic polynomial with coefficients in a Dedekind ring A. If P is a prime ideal and AP denotes the completion of A at P then f(x) is said to be integrally closed at P if AP[X](f(X)) is isomorphic to a product of discrete valuation rings. The purpose of this note is to show that if f(x) appears to be tamely ramified and integrally closed at P (in terms of its discriminant and factorization mod P) then in fact it is.

Mathematical Subject Classification 2000
Primary: 12B10, 12B10
Secondary: 13F05
Received: 22 December 1978
Published: 1 February 1980
Joe Peter Buhler
Center for Communications Research