About: Eakin–Nagata theorem

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

In abstract algebra, the Eakin–Nagata theorem states: given commutative rings such that is finitely generated as a module over , if is a Noetherian ring, then is a Noetherian ring. (Note the converse is also true and is easier.) The theorem is similar to the Artin–Tate lemma, which says that the same statement holds with "Noetherian" replaced by "finitely generated algebra" (assuming the base ring is a Noetherian ring).

Property Value
dbo:abstract
  • In abstract algebra, the Eakin–Nagata theorem states: given commutative rings such that is finitely generated as a module over , if is a Noetherian ring, then is a Noetherian ring. (Note the converse is also true and is easier.) The theorem is similar to the Artin–Tate lemma, which says that the same statement holds with "Noetherian" replaced by "finitely generated algebra" (assuming the base ring is a Noetherian ring). The theorem was first proved in Paul M. Eakin's thesis and later independently by Masayoshi Nagata. The theorem can also be deduced from the characterization of a Noetherian ring in terms of injective modules, as done for example by David Eisenbud in; this approach is useful for a generalization to non-commutative rings. (en)
dbo:wikiPageExternalLink
dbo:wikiPageID
  • 62674651 (xsd:integer)
dbo:wikiPageLength
  • 5681 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1103146576 (xsd:integer)
dbo:wikiPageWikiLink
dbp:authorlink
  • Masayoshi Nagata (en)
dbp:first
  • Masayoshi (en)
dbp:last
  • Nagata (en)
dbp:wikiPageUsesTemplate
dbp:year
  • 1968 (xsd:integer)
dcterms:subject
rdfs:comment
  • In abstract algebra, the Eakin–Nagata theorem states: given commutative rings such that is finitely generated as a module over , if is a Noetherian ring, then is a Noetherian ring. (Note the converse is also true and is easier.) The theorem is similar to the Artin–Tate lemma, which says that the same statement holds with "Noetherian" replaced by "finitely generated algebra" (assuming the base ring is a Noetherian ring). (en)
rdfs:label
  • Eakin–Nagata theorem (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageRedirects of
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License