Subadditive Euclidean norm

This article defines a property that can be evaluated for a Euclidean norm on a commutative unital ring

Definition

Let $R$ be a commutative unital ring and $N$ be a Euclidean norm on $R$. We say that $N$ is subadditive if for any $a,b\in R$ such that $ab(a+b)\neq 0$, we have:

$N(a+b)\leq N(a)+N(b)$.

Relation with other properties

Stronger properties

• Filtrative Euclidean norm