JP Journal of Algebra, Number Theory and Applications
Volume 41, Issue 2, Pages 275 - 287
(February 2019) http://dx.doi.org/10.17654/NT041020275 |
|
ON GALOIS p-ADIC FIELDS OF p-POWER DEGREE
Chad Awtrey, Peter Komlofske, Christian Reese and Janaé Williams
|
Abstract: Let p > 2 be prime. We study the problem of determining defining polynomials of totally ramified Galois extensions of the p-adic numbers of degree pn for some positive integer n. By Local Class Field Theory, this amounts to finding one Eisenstein polynomial for each of the pn isomorphism classes of cyclic extensions of degree pn. The case n = 1 is due to Amano [1]. We give analogous results for the cases n = 2 and n = 3.
|
Keywords and phrases: Eisenstein, p-adic, Galois, totally ramified, cyclic.
|
|
Number of Downloads: 402 | Number of Views: 5245 |
|