Characterizations of a Krull ring $R[X]$
Bull. Korean Math. Soc. 2001 Vol. 38, No. 3, 543-549
Gyu Whan Chang
Kangwon National University
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 $R_M$ 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 : Krull ring, normal ring, overring, factorial ring
MSC numbers : 13A15, 13A18, 13G05
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