A note on tamely ramified polynomials

Joe Peter Buhler

Vol. 86 (1980), No. 2, 421–425

DOI: 10.2140/pjm.1980.86.421

Abstract

Let f(x) be a monic polynomial with coefficients in a Dedekind ring A. If P is a prime ideal and A_P denotes the completion of A at P then f(x) is said to be integrally closed at P if A_P[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

Milestones

Received: 22 December 1978

Published: 1 February 1980