Filtrative Euclidean norm
This article defines a property that can be evaluated for a Euclidean norm on a commutative unital ring
Definition
A Euclidean norm on an integral domain is said to be filtrative if it satisfies the following condition:
The set of elements of norm at most, along with zero, forms an additive subgroup. Thus, the association to each of the corresponding subgroup forms a filtration of additive subgroups of the integral domain.
