Radically perfect prime ideals in polynomial rings

Erdogdu V.

ARCHIV DER MATHEMATIK, cilt.93, ss.213-217, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 93 Konu: 3
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s00013-009-0036-1
  • Sayfa Sayıları: ss.213-217


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 Bezout 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.