Developing Hilbert’s nullstellensatz into categorical adjunction

Abstract EN

This paper includes an improvement of the categorical isomorphism between the category of radical ideals and the category of affine algebraic sets into an adjunction between two functors.

Afterwards, we extend the previous functors by means of expanding our work into the category of all ideals in a polynomial ring in n variables over a fixed algebraically closed field k, in which the radical ideals form a full subcategory of it, in order to produce more generalized adjunction from which we obtain the following results: