## Abstract

Let R=F{x_{ 1}, ..., x_{k}} 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 language | English |
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Pages (from-to) | 116-128 |

Number of pages | 13 |

Journal | Israel Journal of Mathematics |

Volume | 43 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1982 |

## ASJC Scopus subject areas

- General Mathematics