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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 wikiPageLength "1467".
- Coherent_ring wikiPageOutDegree "13".
- Coherent_ring wikiPageRevisionID "545069585".
- Coherent_ring wikiPageWikiLink Category:Ring_theory.
- Coherent_ring wikiPageWikiLink Direct_product.
- Coherent_ring wikiPageWikiLink Direct_sum_of_modules.
- Coherent_ring wikiPageWikiLink Finitely_generated_ideal.
- Coherent_ring wikiPageWikiLink Finitely_generated_module.
- Coherent_ring wikiPageWikiLink Finitely_presented_module.
- Coherent_ring wikiPageWikiLink Flat_module.
- Coherent_ring wikiPageWikiLink Ideal_(ring_theory).
- Coherent_ring wikiPageWikiLink Injective_module.
- Coherent_ring wikiPageWikiLink Left_ideal.
- Coherent_ring wikiPageWikiLink Noetherian_ring.
- Coherent_ring wikiPageWikiLink Ring_(mathematics).
- Coherent_ring wikiPageWikiLink Springer-Verlag.
- Coherent_ring wikiPageWikiLink Springer_Science+Business_Media.
- Coherent_ring wikiPageWikiLink Transactions_of_the_American_Mathematical_Society.
- Coherent_ring wikiPageWikiLinkText "coherence".
- Coherent_ring wikiPageWikiLinkText "coherent ring".
- Coherent_ring wikiPageWikiLinkText "coherent".
- Coherent_ring first "V.E.".
- Coherent_ring hasPhotoCollection Coherent_ring.
- Coherent_ring id "Coherent_ring".
- Coherent_ring last "Govorov".
- Coherent_ring wikiPageUsesTemplate Template:Citation.
- Coherent_ring wikiPageUsesTemplate Template:Harv.
- Coherent_ring wikiPageUsesTemplate Template:Springer.
- Coherent_ring subject Category:Ring_theory.
- Coherent_ring hypernym Ring.
- Coherent_ring type AnatomicalStructure.
- 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 "Coherent ring".
- Coherent_ring sameAs Anneau_cohérent.
- Coherent_ring sameAs 連接環.
- 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.