Factorization of skew polynomials over k((u))
Résumé
Let k be a perfect field of characteristic p > 0, and let K = k((u)) be the field of Laurent series over K. We study the skew polynomial ring K[T, ϕ], where ϕ is an endomorphism of K that extends a Frobenius endomorphism of k. We give a description of the irreducible skew polynomials, develop an analogue of the theory of the Newton polygon in this context, and classify the similarity classes of irreducible elements.
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