Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-31T20:43:54.257Z Has data issue: false hasContentIssue false
  • English
  • Français

PROJECTIVE PRIME IDEALS AND LOCALISATION IN PI-RINGS

Published online by Cambridge University Press:  24 August 2001

A. W. CHATTERS ,
C. R. HAJARNAVIS  and
R. M. LISSAMAN
A. W. CHATTERS
Affiliation:
School of Mathematics, University Walk, Bristol BS8 1TW
C. R. HAJARNAVIS
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
R. M. LISSAMAN
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
Get access

Abstract

The results here generalise [2, Proposition 4.3] and [9, Theorem 5.11]. We shall prove the following.

THEOREM A. Let R be a Noetherian PI-ring. Let P be a non-idempotent prime ideal of R such that PRis projective. Then P is left localisable and RPis a prime principal left and right ideal ring.

We also have the following theorem.

THEOREM B. Let R be a Noetherian PI-ring. Let M be a non-idempotent maximal ideal of R such that MRis projective. Then M has the left AR-property and M contains a right regular element of R.

Information

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 1 - 12
Copyright
The London Mathematical Society 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable