nLab atomic domain

Context

Arithmetic

Algebra

Contents

Definition

An atomic domain is an integral domain in which every cancellative non-unit can be written in at least one way as a finite product of irreducible elements.

Examples

Examples of atomic domains include unique factorization domains and Noetherian domains. More generally, every integral domain satisfying the ascending chain condition on principal ideals is an atomic domain.

References

Last revised on January 11, 2025 at 18:24:54. See the history of this page for a list of all contributions to it.