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Israel Journal of Mathematics

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

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

  • Amiram Braun
Article

Abstract

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)/q=k.dz(R). The last condition is a necessary butnot sufficient condition for contractability ofq fromR.

Keywords

Prime Ideal Maximal Ideal Polynomial Identity Kruli Dimension Integral Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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