Gorenstein Analogue of Auslander's Theorem on the Global Dimension
D Bennis, K Hu, F Wang - Communications in Algebra, 2015 - Taylor & Francis
D Bennis, K Hu, F Wang
Communications in Algebra, 2015•Taylor & FrancisIn this paper, we prove that the Gorenstein analogue of the well-known Auslander's theorem
on the global dimension holds true. Namely, we prove that the Gorenstein global dimension
of a commutative ring R is equal to the supremum of the set of Gorenstein projective
dimensions of all cyclic R-modules.
on the global dimension holds true. Namely, we prove that the Gorenstein global dimension
of a commutative ring R is equal to the supremum of the set of Gorenstein projective
dimensions of all cyclic R-modules.
In this paper, we prove that the Gorenstein analogue of the well-known Auslander's theorem on the global dimension holds true. Namely, we prove that the Gorenstein global dimension of a commutative ring R is equal to the supremum of the set of Gorenstein projective dimensions of all cyclic R-modules.
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