Characterizing cyclic cubic extensions by automorphism polynomials. (English) Zbl 0810.12003

Morton, Patrick

J. Number Theory 49, No. 2, 183-208 (1994).

Let \(K\) be a field of characteristic \(\neq 2\). The author gives a description of abelian extensions of \(K\) having exponent 3, without assuming that \(K\) contains third roots of unity, as is done in Kummer theory. These extensions are shown to be in a one-to-one correspondence with certain groups of two-dimensional matrices over \(K\).

Reviewer: W.Narkiewicz (Wrocław)

MSC:

12F10	Separable extensions, Galois theory
11R20	Other abelian and metabelian extensions
11R16	Cubic and quartic extensions
11C08	Polynomials in number theory

Keywords:

cyclic cubic extensions; automorphism polynomials; periodic points; abelian extensions; Kummer theory