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- Going_up_and_going_down abstract "In commutative algebra, a branch of mathematics, going up and going down are terms which refer to certain properties of chains of prime ideals in integral extensions.The phrase going up refers to the case when a chain can be extended by \"upward inclusion\", while going down refers to the case when a chain can be extended by \"downward inclusion\".The major results are the Cohen–Seidenberg theorems, which were proved by Irvin S. Cohen and Abraham Seidenberg. These are known as the going-up and going-down theorems.".
- Going_up_and_going_down wikiPageID "2083445".
- Going_up_and_going_down wikiPageLength "7372".
- Going_up_and_going_down wikiPageOutDegree "20".
- Going_up_and_going_down wikiPageRevisionID "649212822".
- Going_up_and_going_down wikiPageWikiLink Abraham_Seidenberg.
- Going_up_and_going_down wikiPageWikiLink Category:Commutative_algebra.
- Going_up_and_going_down wikiPageWikiLink Category:Prime_ideals.
- Going_up_and_going_down wikiPageWikiLink Category:Theorems_in_abstract_algebra.
- Going_up_and_going_down wikiPageWikiLink Chain_(disambiguation).
- Going_up_and_going_down wikiPageWikiLink Commutative_algebra.
- Going_up_and_going_down wikiPageWikiLink Flat_module.
- Going_up_and_going_down wikiPageWikiLink Ian_G._Macdonald.
- Going_up_and_going_down wikiPageWikiLink Inclusion_map.
- Going_up_and_going_down wikiPageWikiLink Integral_element.
- Going_up_and_going_down wikiPageWikiLink Irvin_Cohen.
- Going_up_and_going_down wikiPageWikiLink Irving_Kaplansky.
- Going_up_and_going_down wikiPageWikiLink Mathematics.
- Going_up_and_going_down wikiPageWikiLink Michael_Atiyah.
- Going_up_and_going_down wikiPageWikiLink Prime_ideal.
- Going_up_and_going_down wikiPageWikiLink Ring_homomorphism.
- Going_up_and_going_down wikiPageWikiLink Subset.
- Going_up_and_going_down wikiPageWikiLinkText "Cohen-Seidenberg theorems".
- Going_up_and_going_down wikiPageWikiLinkText "Going up and going down".
- Going_up_and_going_down wikiPageWikiLinkText "Going up and going down#Lying over and incomparability".
- Going_up_and_going_down wikiPageWikiLinkText "Going-up and going-down theorems".
- Going_up_and_going_down wikiPageWikiLinkText "Going_up_and_going_down#Lying_over_and_incomparability".
- Going_up_and_going_down wikiPageWikiLinkText "going up and going down properties".
- Going_up_and_going_down wikiPageWikiLinkText "going up and going down".
- Going_up_and_going_down wikiPageWikiLinkText "going up".
- Going_up_and_going_down wikiPageWikiLinkText "going-down property".
- Going_up_and_going_down wikiPageWikiLinkText "going-down theorem".
- Going_up_and_going_down wikiPageWikiLinkText "going-up and going-down theorems".
- Going_up_and_going_down wikiPageWikiLinkText "going-up property".
- Going_up_and_going_down wikiPageWikiLinkText "incomparability".
- Going_up_and_going_down wikiPageUsesTemplate Template:Cite_book.
- Going_up_and_going_down wikiPageUsesTemplate Template:Harv.
- Going_up_and_going_down wikiPageUsesTemplate Template:MR.
- Going_up_and_going_down wikiPageUsesTemplate Template:Reflist.
- Going_up_and_going_down subject Category:Commutative_algebra.
- Going_up_and_going_down subject Category:Prime_ideals.
- Going_up_and_going_down subject Category:Theorems_in_abstract_algebra.
- Going_up_and_going_down hypernym Terms.
- Going_up_and_going_down type Country.
- Going_up_and_going_down type Theorem.
- Going_up_and_going_down comment "In commutative algebra, a branch of mathematics, going up and going down are terms which refer to certain properties of chains of prime ideals in integral extensions.The phrase going up refers to the case when a chain can be extended by \"upward inclusion\", while going down refers to the case when a chain can be extended by \"downward inclusion\".The major results are the Cohen–Seidenberg theorems, which were proved by Irvin S. Cohen and Abraham Seidenberg.".
- Going_up_and_going_down label "Going up and going down".
- Going_up_and_going_down sameAs Q2379132.
- Going_up_and_going_down sameAs Sätze_von_Cohen-Seidenberg.
- Going_up_and_going_down sameAs משפטי_כהן-סיידנברג.
- Going_up_and_going_down sameAs 上昇と下降.
- Going_up_and_going_down sameAs m.06l0__.
- Going_up_and_going_down sameAs Q2379132.
- Going_up_and_going_down wasDerivedFrom Going_up_and_going_down?oldid=649212822.
- Going_up_and_going_down isPrimaryTopicOf Going_up_and_going_down.