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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.
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참고문헌 (16)
참고문헌 신청
H. Bass / 1963 / Big projective modules are free / Illinois J. Math 7:24~31
D. Bennis / 2015 / Gorenstein analogue of Auslander's theorem on the global dimension / Comm. Algebra 43(1):174~181
D. Bennis / 2007 / Strongly Gorenstein projective, injective, and at modules / J. Pure Appl. Algebra 210(2):437~445
E. E. Enochs / 1995 / Gorenstein injective and projective modules / Math. Z 220(4):611~633
H. Holm / 2004 / Gorenstein homological dimensions / J. Pure Appl. Algebra 189(1-3):167~193
D. Bennis / 2015 / Gorenstein analogue of Auslander's theorem on the global dimension / Comm. Algebra 43(1):174~181
D. Bennis / 2007 / Strongly Gorenstein projective, injective, and at modules / J. Pure Appl. Algebra 210(2):437~445
E. E. Enochs / 1995 / Gorenstein injective and projective modules / Math. Z 220(4):611~633
H. Holm / 2004 / Gorenstein homological dimensions / J. Pure Appl. Algebra 189(1-3):167~193
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