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 exp
anding 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.