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 On strongly Gorenstein hereditary rings Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 373-382 https://doi.org/10.4134/BKMS.b180249Published online March 1, 2019 Kui Hu, Hwankoo Kim, Fanggui Wang, Longyu Xu, Dechuan Zhou Southwest University of Science and Technology; Hoseo University; Sichuan Normal University; Southwest University of Science and Technology; 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 an $SG$-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 domains whose ideals are $SG$-projective. Keywords : strongly Gorenstein projective module, strongly Gorenstein hereditary ring, strongly Gorenstein Dedekind domain MSC numbers : 13G05, 13D03 Downloads: Full-text PDF   Full-text HTML