Linearized multivariate skew polynomials and hilbert 90 theorems with multivariate norms
- Autores: Umberto Martínez Peñas
- Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 43, 2018 (Ejemplar dedicado a: Proceedings of the XVI EACA Zaragoza Encuentros de Algebra Computacional y Aplicaciones), págs. 119-122
- Idioma: inglés
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Resumen
We linearize the concept of free multivariate skew polynomials. We give a vector space description of their sets of roots in one conjugacy class, whose univariate counterpart is crucial in applications such as network coding. As a collateral consequence, we derive new Hilbert 90 theorems for general Galois field extensions. In contrast with the homological versions, these are computational theorems based on multivariate norms that reflect the relations among generators of the corresponding Galois group.
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