# Multiplicatively monotone norm

From Commalg

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 **multiplicatively monotone norm** on a commutative unital ring is a function from its nonzero elements to the nonnegative integers with the property that the norm of a product is at least equal to the norms of the factors.

In symbols, it is a function such that for , we have:

.

This definition is typically used for integral domains.