Bulletin of the Korean Mathematical Society (대한수학회보)

The Korean Mathematical Society (대한수학회)
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AN ANDERSON'S THEOREM ON NONCOMMUTATIVE RINGS

Huh, Chan;Kim, Nam-Kyun;Lee, Yang

  • Published : 2008.11.30

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

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References

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