gorenstein flat and gorenstein injective dimensions of simple modules
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abstract
let r be a right gf-closed ring with finite left and right gorenstein global dimension. we prove that if i is an ideal of r such that r/i is a semi-simple ring, then the gorensntein flat dimensnion of r/i as a right r-module and the gorensntein injective dimensnnion of r/i as a left r-module are identical. in particular, we show that for a simple module s over a commutative gorensntein ring r, the gorenstein flat dimension of s equals to the gorenstein injective dimension of s.
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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 39
issue 2 2013
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