Theorem of transition (original) (raw)
In algebra, the theorem of transition is said to hold between commutative rings if 1. * dominates ; i.e., for each proper ideal I of A, is proper and for each maximal ideal of B, is maximal 2. * for each maximal ideal and -primary ideal of , is finite and moreover Given commutative rings such that dominates and for each maximal ideal of such that is finite, the natural inclusion is a faithfully flat ring homomorphism if and only if the theorem of transition holds between .
| Property | Value |
|---|---|
| dbo:abstract | In algebra, the theorem of transition is said to hold between commutative rings if 1. * dominates ; i.e., for each proper ideal I of A, is proper and for each maximal ideal of B, is maximal 2. * for each maximal ideal and -primary ideal of , is finite and moreover Given commutative rings such that dominates and for each maximal ideal of such that is finite, the natural inclusion is a faithfully flat ring homomorphism if and only if the theorem of transition holds between . (en) |
| dbo:wikiPageExternalLink | https://books.google.com/books%3Fid=QmQPAQAAMAAJ |
| dbo:wikiPageID | 62488279 (xsd:integer) |
| dbo:wikiPageLength | 2005 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1088553577 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Commutative_ring dbc:Theorems_in_ring_theory dbr:Faithfully_flat_ring_homomorphism |
| dbp:wikiPageUsesTemplate | dbt:Algebra-stub dbt:Cite_book dbt:Reflist dbt:Short_description dbt:Google_books |
| dct:subject | dbc:Theorems_in_ring_theory |
| rdfs:comment | In algebra, the theorem of transition is said to hold between commutative rings if 1. * dominates ; i.e., for each proper ideal I of A, is proper and for each maximal ideal of B, is maximal 2. * for each maximal ideal and -primary ideal of , is finite and moreover Given commutative rings such that dominates and for each maximal ideal of such that is finite, the natural inclusion is a faithfully flat ring homomorphism if and only if the theorem of transition holds between . (en) |
| rdfs:label | Theorem of transition (en) |
| owl:sameAs | wikidata:Theorem of transition https://global.dbpedia.org/id/C4RCU |
| prov:wasDerivedFrom | wikipedia-en:Theorem_of_transition?oldid=1088553577&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Theorem_of_transition |
| is dbo:wikiPageRedirects of | dbr:The_theorem_of_transition |
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| is foaf:primaryTopic of | wikipedia-en:Theorem_of_transition |