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

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Let R=F{x 1, ..., xk} be a prime affine p.i. ring and S a multiplicative closed set in the center of R, Z(R). The structure of G-rings of the form R s is completely determined. In particular it is proved that Z(R s)-the normalization of Z(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 of q, a prime ideal of Z(R) from R. More precisely, let Q be a prime ideal of R maximal to satisfy QΥ{hooked}Z(R)=q. Then k.d Z(R)/q=k.d R/Q, h(q)=h(Q) and h(q)+k.d Z(R)/q=k.d z(R). The last condition is a necessary but not sufficient condition for contractability of q from R.

Original languageEnglish
Pages (from-to)116-128
Number of pages13
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - Jun 1982

ASJC Scopus subject areas

  • General Mathematics


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