Vipul: New page: {{Euclidean norm property}} ==Definition== Let $R$ be a commutative unital ring and $N$ be a Euclidean norm on $R$ . We say that $N$ is...

2009-01-22T17:17:47Z

New page: {{Euclidean norm property}} ==Definition== Let <math>R</math> be a commutative unital ring and <math>N</math> be a Euclidean norm on <math>R</math>. We say that <math>N</math> is...

New page

{{Euclidean norm property}}

==Definition==

Let <math>R</math> be a [[commutative unital ring]] and <math>N</math> be a [[Euclidean norm]] on <math>R</math>. We say that <math>N</math> is '''subadditive''' if for any <math>a,b \in R</math> such that <math>ab(a+b) \ne 0</math>, we have:

<math>N(a + b) \le N(a) + N(b)</math>.

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Filtrative Euclidean norm]]

Subadditive Euclidean norm - Revision history

Vipul: New page: {{Euclidean norm property}} ==Definition== Let R be a commutative unital ring and N be a Euclidean norm on R. We say that N is...

Vipul: New page: {{Euclidean norm property}} ==Definition== Let $R$ be a commutative unital ring and $N$ be a Euclidean norm on $R$ . We say that $N$ is...