Universally catenary ring: Difference between revisions
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==Definition== | ==Definition== | ||
A commutative unital ring is termed '''universally catenary''' if | A commutative unital ring is termed '''universally catenary''' if it satisfies the following equivalent conditions: | ||
* Every [[finitely generated algebra]] over it is a [[catenary ring]] | |||
* Every polynomial ring in finitely many variables, over it, is a catenary ring | |||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 00:35, 8 January 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 it satisfies the following equivalent conditions:
- Every finitely generated algebra over it is a catenary ring
- Every polynomial ring in finitely many variables, over it, is a catenary ring