Let p be a prime,  the field of p-adic numbers, m a positive integer such that  and  is an Eisenstein polynomial of degree mp. We give necessary and sufficient conditions on the coefficients of  for its Galois group to be cyclic of order mp.

Eisenstein polynomials, p-adic fields, cyclic, totally ramified extensions.

Received: January 2, 2021; Accepted: January 15, 2021; Published: January 25, 2021

How to cite this article: Chad Awtrey and D. Haydn Stucker, Eisenstein polynomials defining cyclic p‑adic fields with minimal wild ramification, JP Journal of Algebra, Number Theory and Applications 49(1) (2021), 93-100. DOI: 10.17654/NT049010093

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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