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A ring $R$ is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L.~Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if $R$ is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.
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참고문헌 (17)
참고문헌 신청
Jianlong Chen / 2004 / On Noetherian rings with essential socle / Journal of the Australian Mathematical Society 76(1):39~50
F. Couchot / 2006 / RD-atness and RD-injectivity / Comm. Algebra 34(10):3675~3689
A. Facchini / 1998 / Module Theory / Birkhauser/Springer Basel AG
Alberto Facchini / 2014 / Rings over which every RD -projective module is a direct sums of cyclically presented modules / Journal of Algebra 401:179~200
Carl Faith / 1966 / On Kothe rings / Mathematische Annalen 164(3):207~212
F. Couchot / 2006 / RD-atness and RD-injectivity / Comm. Algebra 34(10):3675~3689
A. Facchini / 1998 / Module Theory / Birkhauser/Springer Basel AG
Alberto Facchini / 2014 / Rings over which every RD -projective module is a direct sums of cyclically presented modules / Journal of Algebra 401:179~200
Carl Faith / 1966 / On Kothe rings / Mathematische Annalen 164(3):207~212
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