✦ LIBER ✦

Characterizing Cyclic Cubic Extensions by Automorphism Polynomials

✍ Scribed by P. Morton

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 857 KB
Volume: 49
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1994.1089

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✦ Synopsis

The arithmetic of iterated maps is used to characterize the cyclic cubic extensions (F) of a field (\kappa) (char (\kappa \neq 2) ) in terms of the polynomials representing the nontrivial automorphisms of (F / \kappa). This leads to an analogue of Kummer theory for abelian extensions of exponent 3 of (\kappa), whether or not (\kappa) contains a primitive cube root of unity. Such extensions are shown to be in 1-1 correspondence with certain groups of linear fractional transformations defined over (\kappa). 1994 Academic Press, Inc.

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