Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CHARACTERIZATIONS OF A KRULL RING R[X]

  • Published : 2001.08.01
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Abstract

We show that R[X] is a Krull (Resp. factorial) ring if and only if R is a normal Krull (resp, factorial) ring with a finite number of minimal prime ideals if and only if R is a Krull (resp. factorial) ring with a finite number of minimal prime ideals and R(sub)M is an integral domain for every maximal ideal M of R. As a corollary, we have that if R[X] is a Krull (resp. factorial) ring and if D is a Krull (resp. factorial) overring of R, then D[X] is a Krull (resp. factorial) ring.

Keywords

References

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