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- Title
EXTENDED GENUS FIELD OF CYCLIC KUMMER EXTENSIONS OF RATIONAL FUNCTION FIELDS.
- Authors
Curiel-Anaya, Edgar Omar; Maldonado-Ramírez, Myriam Rosalía; Rzedowski-Calderón, Martha
- Abstract
For a cyclic Kummer extension K of a rational function field k is considered, via class field theory, the extended Hilbert class field K+ H of K and the corresponding extended genus field K+ g of K over k, along the lines of the definitions of R. Clement for such extensions of prime degree. We obtain K+ g explicitly. Also, we use cohomology to determine the number of ambiguous classes and obtain a reciprocity law for K=k. Finally, we present a necessary and sufficient condition for a prime of K to decompose fully in K+ g .
- Subjects
RECIPROCITY (Psychology); DEFINITIONS; DEDEKIND sums
- Publication
Palestine Journal of Mathematics, 2023, Vol 12, Issue 4, p440
- ISSN
2219-5688
- Publication type
Article