Israel Journal of Mathematics

, Volume 43, Issue 2, pp 116–128 | Cite as

P.I.G-rings and the contractability of primes

  • Amiram Braun


LetR=F{x 1, …, xk} be a prime affine p.i. ring andS a multiplicative closed set in the center ofR, Z(R). The structure ofG-rings of the formR s is completely determined. In particular it is proved thatZ(R s)—the normalization ofZ(R s) —is a prüfer ring, 1≦k.d(R s)≦p.i.d(R s) and the inequalities can be strict. We also obtain a related result concerning the contractability ofq, a prime ideal ofZ(R) fromR. More precisely, letQ be a prime ideal ofR maximal to satisfyQϒZ(R)=q. Then k.dZ(R)/q=k.dR/Q, h(q)=h(Q) andh(q)+k.dZ(R)/ The last condition is a necessary butnot sufficient condition for contractability ofq fromR.


Prime Ideal Maximal Ideal Polynomial Identity Kruli Dimension Integral Extension 
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Copyright information

© Hebrew University 1982

Authors and Affiliations

  • Amiram Braun
    • 1
  1. 1.Department of MathematicsHaifa UniversityHaifaIsrael

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