On strongly Gorenstein hereditary rings
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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.
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.
참고문헌 (16)
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