Nonnegative norm

This article defines a property that can be evaluated for a norm on a commutative unital ring: a function from the nonzero elements of the ring to the integers.
View a complete list of properties of norms

Definition

A norm on a commutative unital ring $R$ (i.e., a function from the nonzero elements of $R$ to the integers) is termed nonnegative if it takes nonnegative values on all nonzero elements of the ring.

Relation with other properties

Stronger properties

• Positive norm
• Euclidean norm
• Dedekind-Hasse norm