Author:
Ding Nanqing,Chen Jianlong
Abstract
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.
Publisher
Cambridge University Press (CUP)
Cited by
11 articles.
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1. On w-FI-flat and w-FI-injective modules;ANNALI DELL'UNIVERSITA' DI FERRARA;2022-02-25
2. w-FP-projective Modules and Dimensions;Springer Proceedings in Mathematics & Statistics;2022
3. Strongly Max-Flat Modules;Communications in Algebra;2013-03-06
4. Gorenstein Flat Covers over GF-Closed Rings;Communications in Algebra;2012-05
5. HOMOLOGICAL PROPERTIES OF MODULES OVER DING-CHEN RINGS;Journal of the Korean Mathematical Society;2012-01-01