Automorphism-invariant Euclidean norm: Difference between revisions
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{{Euclidean norm | {{curing-norm property conjunction|automorphism-invariant norm|Euclidean norm}} | ||
==Definition== | ==Definition== | ||
A [[ | A [[norm on a commutative unital ring]] is termed an '''automorphism-invariant Euclidean norm''' or a '''characteristic Euclidean norm''' if it satisfies the following two conditions: | ||
* It is an [[automorphism-invariant norm]]: The image of an element of the ring under an automorphism has the same norm as the element. | |||
* It is a [[Euclidean norm]]. | |||
==Relation with other properties== | |||
===Weaker properties=== | |||
* [[Stronger than::Automorphism-invariant Dedekind-Hasse norm]] | |||
Latest revision as of 21:08, 23 January 2009
This article defines a property of a norm on a commutative unital ring obtained as the conjunction of two properties: automorphism-invariant norm and Euclidean norm.
View a complete list of such conjunctions | View a complete list of properties of norms in commutative unital rings
Definition
A norm on a commutative unital ring is termed an automorphism-invariant Euclidean norm or a characteristic Euclidean norm if it satisfies the following two conditions:
- It is an automorphism-invariant norm: The image of an element of the ring under an automorphism has the same norm as the element.
- It is a Euclidean norm.