On quasihereditary rings

Authors:
W. D. Burgess and K. R. Fuller

Journal:
Proc. Amer. Math. Soc. **106** (1989), 321-328

MSC:
Primary 16A66; Secondary 16A32

MathSciNet review:
964453

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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 is semiprimary of global dimension 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 is quasihereditary then the Cartan determinant conjecture is true for (i.e., ); 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-relations algebra in fact) of global dimension 3 which is not quasihereditary.

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0964453-8

Keywords:
Quasihereditary rings,
Cartan determinant,
serial ring

Article copyright:
© Copyright 1989
American Mathematical Society