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### A structure theorem for noetherian PI rings with global dimension two

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UNSPECIFIED.
(1999)
*A structure theorem for noetherian PI rings with global dimension two.*
JOURNAL OF ALGEBRA, 215
(1).
pp. 248-289.
ISSN 0021-8693

**Full text not available from this repository.**

## Abstract

Let A be the Artin radical of a Noetherian ring R of global dimension two. We show that A = ReR where e is an idempotent; A contains a heredity chain of ideals and the global dimensions of the rings R/A and eRe cannot exceed two. Assume further than R isa polynomial identity ring. Let P be a minimal prime ideal of R. Then P = P-2 and the global dimension of R/P is also bounded by two. In particular, if the Krull dimension of R/P equals two for all minimal primes P then R is a semiprime ring. In general, every clique of prime ideals in R is finite and in the affine case R is a finite module over a commutative affine subring. Additionally, when A = 0, the ring R has an Artinian quotient ring and we provide a structure theorem which shows that R is obtained by a certain subidealizing process carried out on rings involving Dedekind prime rings and other homologically homogeneous rings. (C) 1999 Academic Press.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Journal or Publication Title: | JOURNAL OF ALGEBRA |

Publisher: | ACADEMIC PRESS INC |

ISSN: | 0021-8693 |

Official Date: | 1 May 1999 |

Volume: | 215 |

Number: | 1 |

Number of Pages: | 42 |

Page Range: | pp. 248-289 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/14594 |

Data sourced from Thomson Reuters' Web of Knowledge

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