Universally catenary ring: Difference between revisions
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==Definition== | ==Definition== | ||
A commutative unital ring is termed '''universally catenary''' if it | A [[commutative unital ring]] is termed '''universally catenary''' if every [[finitely generated algebra]] over it is a [[catenary ring]]. | ||
Since catenary rings are, by definition, Noetherian, so are universally catenary rings. | |||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 21:54, 9 March 2008
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
Definition
A commutative unital ring is termed universally catenary if every finitely generated algebra over it is a catenary ring.
Since catenary rings are, by definition, Noetherian, so are universally catenary rings.
Relation with other properties
Stronger properties
Weaker properties
Metaproperties
Closure under taking quotient rings
This property of commutative unital rings is quotient-closed: the quotient ring of any ring with this property, by any ideal in it, also has this property
View other quotient-closed properties of commutative unital rings