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Rings whose quasi-injective modules are injective. (English) Zbl 0214.05605


MSC:

16P50 Localization and associative Noetherian rings
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
16P40 Noetherian rings and modules (associative rings and algebras)
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References:

[1] Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466 – 488. · Zbl 0094.02201
[2] K. A. Byrd, When are quasi-injectives injective?, Canad. Math. Bull. 15 (1972), 599 – 600. · Zbl 0248.16016 · doi:10.4153/CMB-1972-104-1
[3] John H. Cozzens, Homological properties of the ring of differential polynomials, Bull. Amer. Math. Soc. 76 (1970), 75 – 79. · Zbl 0213.04501
[4] A. W. Goldie, Semi-prime rings with maximum condition, Proc. London Math. Soc. (3) 10 (1960), 201 – 220. · Zbl 0091.03304 · doi:10.1112/plms/s3-10.1.201
[5] R. P. Kurshan, Rings whose cyclic modules have finitely generated socle, J. Algebra 15 (1970), 376 – 386. · Zbl 0199.35503 · doi:10.1016/0021-8693(70)90066-9
[6] Eben Matlis, Injective modules over Noetherian rings, Pacific J. Math. 8 (1958), 511 – 528. · Zbl 0084.26601
[7] D. B. Webber, Ideals and modules of simple Noetherian hereditary rings, J. Algebra 16 (1970), 239 – 242. · Zbl 0211.06201 · doi:10.1016/0021-8693(70)90029-3
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