A structure theorem for noetherian PI rings with global dimension two
UNSPECIFIED. (1999) A structure theorem for noetherian PI rings with global dimension two. JOURNAL OF ALGEBRA, 215 (1). pp. 248-289. ISSN 0021-8693Full text not available from this repository.
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|
|Date:||1 May 1999|
|Number of Pages:||42|
|Page Range:||pp. 248-289|
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