NDLI: Radically perfect prime ideals in polynomial rings

Content Provider	Springer Nature Link
Author	Erdoğdu, Vahap
Copyright Year	2009
Abstract	We call an ideal I of a commutative ring R radically perfect if among the ideals of R whose radical is equal to the radical of I the one with the least number of generators has this number of generators equal to the height of I. Let R be a Noetherian integral domain of Krull dimension one containing a field of characteristic zero. Then each prime ideal of the polynomial ring R[X] is radically perfect if and only if R is a Dedekind domain with torsion ideal class group. We also show that over a finite dimensional Bézout domain R, the polynomial ring R[X] has the property that each prime ideal of it is radically perfect if and only if R is of dimension one and each prime ideal of R is the radical of a principal ideal.
Ending Page	217
Page Count	5
Starting Page	213
File Format	PDF
ISSN	0003889X
e-ISSN	14208938
Journal	Archiv der Mathematik
Issue Number	3
Volume Number	93
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2009-08-26
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Polynomials over commutative rings Polynomial rings Radically perfect ideals Plane and space curves Dimension theory, depth, related rings (catenary, etc.) Polynomial rings and ideals; rings of integer-valued polynomials Dedekind, PrÃ¼fer, Krull and Mori rings and their generalizations Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Radically perfect prime ideals in polynomial rings