On quasihereditary rings-Reference-Cited by-同舟云学术

On quasihereditary rings

Published:1989 Issue:2 Volume:106 Page:321-328
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Burgess W. D.,Fuller K. R.

Abstract

The notion of a quashereditary semiprimary ring was introduced by Cline, Parshall and Scott and was studied extensively by Dlab and Ringel. It is known that if R R is semiprimary of global dimension ≤ 2 \leq 2 then it is quasihereditary and that there is a serial ring of global dimension 4 which is not. This paper establishes three principal results: If R R is quasihereditary then the Cartan determinant conjecture is true for R R (i.e., C ( R ) = 1 C(R) = 1 ); a serial ring is quasihereditary iff it has a heredity ideal; in particular, every serial ring of global dimension 3 is quasihereditary; and there is a ring (a 0 0 -relations algebra in fact) of global dimension 3 which is not quasihereditary.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1989-106-02/S0002-9939-1989-0964453-8/S0002-9939-1989-0964453-8.pdf

Reference12 articles.

1. The Cartan matrix as an indicator of finite global dimension for Artinian rings;Burgess, W. D.;Proc. Amer. Math. Soc.,1985

2. Finite-dimensional algebras and highest weight categories;Cline, E.;J. Reine Angew. Math.,1988

3. V. Dlab and C. Ringel, Heredity ideals, typescript 1987, 11 pages.

4. \bysame, Quasi-hereditary algebras, typescript 1987, 7 pages.

5. \bysame, Every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring, typescript 1987, 7 pages.

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