A right PCI ring is right Noetherian. (English) Zbl 0425.16022
MSC:
16D70 | Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) |
16D50 | Injective modules, self-injective associative rings |
16P40 | Noetherian rings and modules (associative rings and algebras) |
Citations:
Zbl 0169.356References:
[1] | John Cozzens and Carl Faith, Simple Noetherian rings, Cambridge University Press, Cambridge-New York-Melbourne, 1975. Cambridge Tracts in Mathematics, No. 69. · Zbl 0314.16001 |
[2] | Lawrence Levy, Torsion-free and divisible modules over non-integral-domains, Canad. J. Math. 15 (1963), 132 – 151. · Zbl 0108.04001 · doi:10.4153/CJM-1963-016-1 |
[3] | B. L. Osofsky, Noninjective cyclic modules, Proc. Amer. Math. Soc. 19 (1968), 1383 – 1384. · Zbl 0169.35602 |
[4] | Bo Stenström, Rings of quotients, Springer-Verlag, New York-Heidelberg, 1975. Die Grundlehren der Mathematischen Wissenschaften, Band 217; An introduction to methods of ring theory. · Zbl 0296.16001 |
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