On the degree of the splitting field of an irreducible binomial

David Andrew Gay and William Yslas Vélez

Vol. 78 (1978), No. 1, 117–120

DOI: 10.2140/pjm.1978.78.117

Abstract

Let x^m − a be irreducible over a field F. We give a new proof of Darbi’s formula for the degree of the splitting field of x^m −a and investigate some of its properties. We give a more explicit formula in case the only roots of unity in F are ±1.

Mathematical Subject Classification 2000

Primary: 12E10

Milestones

Received: 16 September 1977

Revised: 10 March 1978

Published: 1 September 1978