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- Q4801178 subject Q7036089.
- Q4801178 subject Q8399470.
- Q4801178 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.".
- Q4801178 wikiPageWikiLink Q1225713.
- Q4801178 wikiPageWikiLink Q1455652.
- Q4801178 wikiPageWikiLink Q159943.
- Q4801178 wikiPageWikiLink Q161172.
- Q4801178 wikiPageWikiLink Q190109.
- Q4801178 wikiPageWikiLink Q44649.
- Q4801178 wikiPageWikiLink Q57283.
- Q4801178 wikiPageWikiLink Q7036089.
- Q4801178 wikiPageWikiLink Q8399470.
- Q4801178 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.".
- Q4801178 label "Artinian ideal".