A Family of Algebraically Closed Fields Containing Polynomials in Several Variables
Fuensanta Aroca, Giovanna Ilardi · Communications in Algebra · 2009
We introduce a family of fields of series with support in strongly convex rational cones. All these fields contain polynomials in several variables. We prove that they are algebraically closed with a construction that is analogous to the Newton polygon for algebraic curves. As a corollary, we show the existence of fractional power solutions with support in cones for systems of equations.