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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
DOI: https://doi.org/10.1090/S0002-9939-1989-0964453-8
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 $ R$ is semiprimary of global dimension $ \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$ is quasihereditary then the Cartan determinant conjecture is true for $ R$ (i.e., $ 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-relations algebra in fact) of global dimension 3 which is not quasihereditary.


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Additional Information

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

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