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- Coherent_ring abstract "In mathematics, a (left) coherent ring is a ring in which every finitely generated left ideal is finitely presented. Many theorems about finitely generated modules over Noetherian rings can be extended to finitely presented modules over coherent rings. Every left Noetherian ring is left-coherent. The ring of polynomials in an infinite number of variables is an example of a left-coherent ring that is not left Noetherian.A ring is left coherent if and only if every direct product of flat right modules is flat (Chase 1960), (Anderson & Fuller 1992, p. 229). Compare this to: A ring is left Noetherian if and only if every direct sum of injective left modules is injective.".
- Coherent_ring wikiPageID "14777654".
- Coherent_ring wikiPageRevisionID "545069585".
- Coherent_ring first "V.E.".
- Coherent_ring hasPhotoCollection Coherent_ring.
- Coherent_ring id "Coherent_ring".
- Coherent_ring last "Govorov".
- Coherent_ring subject Category:Ring_theory.
- Coherent_ring comment "In mathematics, a (left) coherent ring is a ring in which every finitely generated left ideal is finitely presented. Many theorems about finitely generated modules over Noetherian rings can be extended to finitely presented modules over coherent rings. Every left Noetherian ring is left-coherent.".
- Coherent_ring label "Anneau cohérent".
- Coherent_ring label "Coherent ring".
- Coherent_ring sameAs Anneau_cohérent.
- Coherent_ring sameAs m.03gxpwf.
- Coherent_ring sameAs Q2851410.
- Coherent_ring sameAs Q2851410.
- Coherent_ring wasDerivedFrom Coherent_ring?oldid=545069585.
- Coherent_ring isPrimaryTopicOf Coherent_ring.