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FINITE CYCLIC TAME EXTENSIONS OF k_p((t))

ULRICA WILSON

Mathematics Department, Morehouse College, 830 Westview Drive, Atlanta, Georgia 30314, U.S.A.

https://doi.org/10.1142/S0219498808002722Cited by:0 (Source: Crossref)

Abstract

Let p be a prime number and let ℚ/ℤ′ be the elements in ℚ/ℤ of order prime to p. Let , where c is a prime power of p. We use characters and valuation theory to prove that Δ is a parameter space for the cyclic tame extensions of the formal Laurent series field k_p((t)) of degree prime to p. Furthermore, we construct the cyclic tame extension corresponding to a given triple in Δ. The structure of finite cyclic tame extensions of the p-adic number fields was thoroughly investigated by A. A. Albert in 1935. Here we get the same result as consequence of our main theorem.

Keywords:

AMSC: 12F10, 11R21, 11S15

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