nLab coherent ring




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.


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