Zero-dimensional ring

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This article is about a standard (though not very rudimentary) definition in commutative algebra. The article text may, however, contain more than just the basic definition
View a complete list of semi-basic definitions on this wiki
This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
View all properties of commutative unital rings
VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions
This property of commutative unital rings is completely determined by the spectrum, viewed as an abstract topological space. The corresponding property of topological spaces is: T1 space


View other properties of commutative unital rings determined by the spectrum

Any integral domain satisfying this property of commutative unital rings, must be a field

Definition

Symbol-free definition

A commutative unital ring is termed zero-dimensional if it satisfies the following equivalent conditions:

Relation with other properties

Conjunction with other properties

Stronger properties

Weaker properties