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Global dimension of factor rings

Published online by Cambridge University Press:  17 April 2009

Yasuyuki Hirano ,
Jae Keol Park  and
Klaus W. Roggenkamp
Yasuyuki Hirano
Affiliation:
Department of MathematicsOkayama UniversityOkayama 700, Japan
Jae Keol Park
Affiliation:
Mathematisches Institut BUniversitāt Stuttgart7 Stuttgart 80, Germany
Klaus W. Roggenkamp
Affiliation:
Department of MathematicsBusan National UniversityBusan 609-735, Korea
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Let R be a right Noetherian ring with right global dimension bounded by 2, which is integral over its centre, and let a be a regular non-unit element in R. Then R/a; R is right hereditary if and only if a; is not in the square of any maximal ideal of R. More generally, we compare for a right Noetherian ring R which is integral over its center, the global dimension of R with the global dimension of R/(a1R + a2R + … + arR) for a regular R-sequence {ai}, which will allow us to give a considerable extension of a result of Hillman.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 399 - 411
Copyright
Copyright © Australian Mathematical Society 1994

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