In commutative algebra, a Zariski ring is a commutative Noetherian topological ring A whose topology is defined by an ideal a {\displaystyle {\mathfrak...

primarily by Oscar Zariski and later generalized for making the set of prime ideals of a commutative ring (called the spectrum of the ring) a topological...

an ideal of }}R{\big \}}.} This topology is called the Zariski topology. A basis for the Zariski topology can be constructed as follows. For f ∈ R {\displaystyle...

Formal scheme Profinite integer Locally compact field Zariski ring Linear topology Quasi-unmixed ring "Stacks Project — Tag 0316". stacks.math.columbia.edu...

rings was introduced by Wolfgang Krull in 1938 under the name Stellenringe. The English term local ring is due to Zariski. A ring R is a local ring if...

valuation rings in algebraic geometry Does there exist a Riemann surface corresponding to every field extension? Any other hypothesis needed? Zariski & Samuel...

Zariski ring Zariski tangent space Zariski surface Zariski topology Zariski–Riemann surface Zariski space (disambiguation) Zariski's lemma Zariski's main...

evaluating M at P is n − dim Y. Zariski proved that Y is nonsingular at P if and only if the local ring of Y at P is regular. (Zariski observed that this can fail...

commutative algebra imply the geometric forms of Zariski's main theorem, including: A normal local ring is unibranch, which is a variation of the statement...

Euclidean topology, or the Zariski topology, and in either case one would obtain a topological ring. A λ-ring is a commutative ring R together with operations...