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- Artinian_ideal abstract "In abstract algebra, an Artinian ideal, named after Emil Artin, is encountered in ring theory, in particular, with polynomial rings.Given a polynomial ring R = k[X1, ... Xn] where k is some field, an Artinian ideal is an ideal I in R for which the Krull dimension of the quotient ring R/I is 0. Also, less precisely, one can think of an Artinian ideal as one that has at least each indeterminate in R raised to a power greater than 0 as a generator. If an ideal is not Artinian, one can take the Artinian closure of it as follows. First, take the least common multiple of the generators of the ideal. Second, add to the generating set of the ideal each indeterminate of the LCM with its power increased by 1 if the power is not 0 to begin with. An example is below.".
- Artinian_ideal wikiPageID "20674787".
- Artinian_ideal wikiPageLength "2133".
- Artinian_ideal wikiPageOutDegree "9".
- Artinian_ideal wikiPageRevisionID "662546842".
- Artinian_ideal wikiPageWikiLink Abstract_algebra.
- Artinian_ideal wikiPageWikiLink Category:Commutative_algebra.
- Artinian_ideal wikiPageWikiLink Category:Ring_theory.
- Artinian_ideal wikiPageWikiLink Emil_Artin.
- Artinian_ideal wikiPageWikiLink Field_(mathematics).
- Artinian_ideal wikiPageWikiLink Ideal_(ring_theory).
- Artinian_ideal wikiPageWikiLink Krull_dimension.
- Artinian_ideal wikiPageWikiLink Polynomial_ring.
- Artinian_ideal wikiPageWikiLink Ring_(mathematics).
- Artinian_ideal wikiPageWikiLinkText "Artinian ideal".
- Artinian_ideal hasPhotoCollection Artinian_ideal.
- Artinian_ideal wikiPageUsesTemplate Template:Abstract-algebra-stub.
- Artinian_ideal wikiPageUsesTemplate Template:Cite_arxiv.
- Artinian_ideal subject Category:Commutative_algebra.
- Artinian_ideal subject Category:Ring_theory.
- Artinian_ideal comment "In abstract algebra, an Artinian ideal, named after Emil Artin, is encountered in ring theory, in particular, with polynomial rings.Given a polynomial ring R = k[X1, ... Xn] where k is some field, an Artinian ideal is an ideal I in R for which the Krull dimension of the quotient ring R/I is 0. Also, less precisely, one can think of an Artinian ideal as one that has at least each indeterminate in R raised to a power greater than 0 as a generator.".
- Artinian_ideal label "Artinian ideal".
- Artinian_ideal sameAs m.0522jmb.
- Artinian_ideal sameAs Q4801178.
- Artinian_ideal sameAs Q4801178.
- Artinian_ideal wasDerivedFrom Artinian_ideal?oldid=662546842.
- Artinian_ideal isPrimaryTopicOf Artinian_ideal.