The Library
A structure theorem for noetherian PI rings with global dimension two
Tools
Tools
Tools
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 |
| 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
Actions (login required)
 |
View Item |
