Zariski topology [SEP] named after
Zariski topology
In algebraic geometry and commutative algebra, the Zariski topology is a topology on algebraic varieties, introduced primarily by Oscar Zariski and later generalized for making the set of prime ideals of a commutative ring a topological space, called the spectrum of the ring.
The Zariski topology allows tools from topology to be used to study algebraic varieties, even when the underlying field is not a topological field. This is one of the basic ideas of scheme theory, which allows one to build general algebraic varieties by gluing together affine
Zariski ring
In commutative algebra, a Zariski ring is a commutative Noetherian topological ring "A" whose topology is defined by an ideal formula_1 contained in the Jacobson radical, the intersection of all maximal ideals. They were introduced by under the name "semi-local ring" which now means something different, and named "Zariski rings" by . Examples of Zariski rings are noetherian local rings with the topology induced by the maximal ideal, and formula_1-adic completions of Noetherian rings.
Let "A" be a Noetherian topological