On strongly Gorenstein hereditary rings
Bull. Korean Math. Soc.
Published online 2018 Nov 09
Kui Hu, Hwankoo Kim, Fanggui Wang, Longyu Xu, and Dechuan Zhou
Hoseo University, Sichuan Normal University, Southwest University of Science and Technology
Abstract : In this note, we mainly discuss strongly Gorenstein hereditary rings.We prove that for any ring, the class of $SG$-projective modules and the class of $G$-projective modules coincide if and only if the class of $SG$-projective modules is closed under extension. From this we get that a ring is a $SG$-hereditary ring if and only if every ideal is $G$-projective and the class of $SG$-projective modules is closed under extension. We also give some examples of $SG$-Dedekind domains which are not Dedekind domains.
Keywords : strongly Gorenstein projective module, strongly Gorenstein hereditary ring, strongly Gorenstein Dedekind domain
MSC numbers : 13G05, 13D03
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