## 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 is a 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.

Original language | English |
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Pages (from-to) | 248-289 |

Number of pages | 42 |

Journal | Journal of Algebra |

Volume | 215 |

Issue number | 1 |

DOIs | |

State | Published - 1 May 1999 |

### Bibliographical note

Funding Information:* This work was partially supported by an EPSRC grant at the University of Warwick. The first author thanks the Mathematics Institute at the University of Warwick for its hospitality.

## ASJC Scopus subject areas

- Algebra and Number Theory