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AN ANDERSON`S THEOREM ON NONCOMMUTATIVE RINGS
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 Title & Authors
AN ANDERSON`S THEOREM ON NONCOMMUTATIVE RINGS
Huh, Chan; Kim, Nam-Kyun; Lee, Yang;
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 Abstract
Let R be a ring and I be a proper ideal of R. For the case of R being commutative, Anderson proved that (*) there are only finitely many prime ideals minimal over I whenever every prime ideal minimal over I is finitely generated. We in this note extend the class of rings that satisfies the condition (*) to noncommutative rings, so called homomorphically IFP, which is a generalization of commutative rings. As a corollary we obtain that there are only finitely many minimal prime ideals in the polynomial ring over R when every minimal prime ideal of a homomorphically IFP ring R is finitely generated.
 Keywords
commutative ring;(homomorphically) IFP ring;minimal prime ideal;
 Language
English
 Cited by
 References
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