Automorphism-invariant Euclidean norm
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.