nLab
coherent ring

Contents

Contents

Definition

A ring is (left) coherent if every finitely generated (left) ideal of this ring is finitely presented. Equivalently, a ring is coherent if and only if it is a (left) coherent module over itself.

Every (left) noetherian ring is a coherent ring.

Lombardi & Quitté 2015 argue that coherent rings are more suited to constructive mathematics than noetherian rings. This is probably connected to the importance of coherent sheaves.

References

Last revised on October 1, 2021 at 11:35:11. See the history of this page for a list of all contributions to it.