Article contents
The homological dimensions of simple modules
Published online by Cambridge University Press: 17 April 2009
Extract
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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