• Corpus ID: 252531354

Factorization of skew polynomials over k((u))

@inproceedings{Borgne2022FactorizationOS,
  title={Factorization of skew polynomials over k((u))},
  author={J{\'e}r{\'e}my Le Borgne},
  year={2022}
}
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. 

References

SHOWING 1-10 OF 10 REFERENCES

Factoring in Skew-Polynomial Rings over Finite Fields

Efficient algorithms are presented for factoring polynomials in the skew-polynomial ringFx;?, a non-commutative generalization of the usual ring of polynomialsFx, whereFis a finite field and ?:F?Fis

On the structure of some moduli spaces of finite flat group schemes

Let p be an odd prime and k a finite field of characteristic p. Let W = W (k) be the ring of Witt vectors with coefficients in k and K0 = W [ 1 p ] its fraction field. We consider a finite, totally

A new faster algorithm for factoring skew polynomials over finite fields

Coding with skew polynomial rings

Fast Multiplication for Skew Polynomials

The algorithms improve the best known complexity for various arithmetics problems, and reaches the optimal asymptotic complexity bound for large degree.

Finite-dimensional division algebras over fields

Skew Polynomials and Division Algebras.- Brauer Factor Sets and Noether Factor Sets.- Galois Descent and Generic Splitting Fields.- p-Algebras.- Simple Algebras with Involution.

P-ADIC Properties of Modular Schemes and Modular Forms

This expose represents an attempt to understand some of the recent work of Atkin, Swinnerton-Dyer, and Serre on the congruence properties of the q-expansion coefficients of modular forms from the

Theory of Non-Commutative Polynomials

Theory of codes with maximum rank distance

  • Probl. Inf. Transm.,
  • 1985