Filtrative 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 is termed filtrative if it is a function from the nonzero elements of the ring to nonnegative integers, and further, for any natural number $n$, the set of elements with norm less than $n$, along with zero, form an additive subgroup of the ring.

Relation with other properties

Stronger properties

• Filtrative Euclidean norm