Algebraic geometry
The notion of a spectrum is the common basis of commutative algebra and algebraic geometry. Algebraic geometry proceeds by endowing Spec "R" with a sheaf formula_149 (an entity that collects functions defined locally, i.e. on varying open subsets). The datum of the space and the sheaf is called an affine scheme. Given an affine scheme, the underlying ring "R" can be recovered as the global sections of formula_149. Moreover, this one-to-one correspondence between rings and affine schemes is also compatible with ring homomorphisms: any "f" : "R" → "S" gives rise to a continuous map in the opposite direction