Zariski ring

In commutative algebra, a Zariski ring is a commutative Noetherian topological ring A whose topology is defined by an ideal m contained in the Jacobson radical, the intersection of all maximal ideals. They were introduced by Oscar Zariski (1946) under the name "semi-local ring" which now means something different, and named "Zariski rings" by Samuel (1953). Examples of Zariski rings are noetherian local rings and -adic completions of noetherian rings.

Let A be a noetherian ring and its -adic completion. Then the following are equivalent.


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