Resumen de Linearized multivariate skew polynomials and hilbert 90 theorems with multivariate norms
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.
