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The homological dimensions of simple modules

Published online by Cambridge University Press:  17 April 2009

Nanqing Ding  and
Jianlong Chen
Nanqing Ding
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210008, Peoples Republic of China
Jianlong Chen
Affiliation:
Department of Mathematics and Mechanics, Southeast University, Nanjing 210018, Peoples Republic of China
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We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals the supremum of the flat (or (FP–)injective) dimensions of the simple R-modules; (b) if R is right semi-artinian, the weak (respectively, the right) global dimension of R equals the supremum of the flat (respectively, projective) dimensions of the simple right R-modules; (c) if R is right semi-artinian and right coherent, the weak global dimension of R equals the supremum of the FP-injective dimensions of the simple right R-modules.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 265 - 274
Copyright
Copyright © Australian Mathematical Society 1993

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