NONCOMMUTATIVE POLYNOMIAL MAPS

DOI10.1142/S0219498812500764zbMath1256.16017arXiv1208.0112OpenAlexW2963005667MaRDI QIDQ2909806

André Leroy

Publication date: 6 September 2012

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.0112

zbMATH Keywords

finite fieldsOre extensionspolynomial mapsfactorizations of polynomials

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Polynomials in general fields (irreducibility, etc.) (12E05)

Related Items (18)

Zeros with multiplicity, Hasse derivatives and linear factors of general skew polynomials ⋮ On the dual codes of skew constacyclic codes ⋮ Skew and linearized Reed-Solomon codes and maximum sum rank distance codes over any division ring ⋮ Matrices that are integral over the base ring ⋮ Some properties of skew codes over finite fields ⋮ Finite nonassociative algebras obtained from skew polynomials and possible applications to \((f,\sigma,\delta)\)-codes ⋮ Zeros, factorizations and least common multiples of quaternion polynomials ⋮ On the intersection of left and right ideals in the ring of quaternion polynomials ⋮ Exponents of skew polynomials. ⋮ Evaluation of iterated Ore polynomials and skew Reed-Muller codes ⋮ A note on integer-valued skew polynomials ⋮ Confluent Vandermonde matrices, divided differences, and Lagrange–Hermite interpolation over quaternions ⋮ Pseudo-linear algebra over a division ring ⋮ Factorization theory: from commutative to noncommutative settings. ⋮ Roos bound for skew cyclic codes in Hamming and rank metric ⋮ \(( \sigma, \delta )\)-skew quasi-cyclic codes over the ring \(\mathbb{Z}_4+u\mathbb{Z}_4 \) ⋮ Exponents of skew polynomials over periodic rings ⋮ Matroidal root structure of skew polynomials over finite fields

Cites Work

• Coding with skew polynomial rings
• Skew-cyclic codes
• Vandermonde and Wronskian matrices over division rings
• Wedderburn polynomials over division rings. I.
• Theory of non-commutative polynomials
• Pseudo-linear transformations
• Algebraic andF-Independent Sets in 2-Firs
• NONCOMMUTATIVE SYMMETRIC FUNCTIONS AND W-POLYNOMIALS

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