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On rings with restricted minimum condition

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References

  1. G. F. Birkenmeier, Baer rings and quasi-continuous rings have a MDSN. Pacific J. Math.97, 283–292 (1981).

    Google Scholar 

  2. A. W. Chatters, A characterisation of right noetherian rings. Quart. J. Math. Oxford (2)33, 65–69 (1982).

    Google Scholar 

  3. A. W. Chatters andC. R. Hajanavis, Rings in which every complement right ideal is a direct summand. Quart. J. Oxford (2)28, 61–80 (1977).

    Google Scholar 

  4. A. W.Chatters and C. R.Hajanavis, Rings with chain conditions. London 1980.

  5. J. H.Cozzens and C.Faith, Simple noetherian rings. Cambridge 1975.

  6. R. F. Damiano, A right PCI ring is right noetherian. Proc. Amer. Math. Soc.77, 11–14 (1979).

    Google Scholar 

  7. Dinh van Huynh andNguyen V. Dung, A characterization of right artinian rings. Glasgow Math. J.30, 67–73 (1988).

    Google Scholar 

  8. C.Faith, Algebra II: Ring Theory. Berlin-Heidelberg-New York 1976.

  9. V. K. Goel andS. K. Jain, π-injective modules and rings whose cyclics are π-injective. Comm. Algebra6, 59–73 (1978).

    Google Scholar 

  10. A. W. Goldie, Semiprime rings with maximum condition. Proc. London Math. Soc.42, 201–220 (1960).

    Google Scholar 

  11. K. R.Goodearl, Singular torsion and splitting properties. Mem. Amer. Math. Soc.124, Providence 1972.

  12. M. Harada andK. Oshiro, On extending property on direct sums of uniform modules. Osaka J. Math.18, 767–785 (1981).

    Google Scholar 

  13. C. Hopkins, Rings with minimal condition for left ideals. Ann. of Math.40, 712–730 (1939).

    Google Scholar 

  14. A.Kertész (Editor), Proc. Colloq. Math. Soc. Bolayai, 6. Rings Modules and Radicals. Amsterdam-London 1973.

  15. G. Michler andO. E. Villamayor, On rings whose simple modules are injective. J. Algebra25, 185–201 (1973).

    Google Scholar 

  16. B. L. Osofsky, Rings all of whose finitely generated modules are injective. Pacific J. Math14, 645–650 (1964).

    Google Scholar 

  17. F. L. Sandomierski, Non-singular rings. Proc. Amer. Math. Soc.19, 225–230 (1968).

    Google Scholar 

  18. S. Singh, On a Warfield's theorem on hereditary rings. Arch. Math.39, 306–311 (1982).

    Google Scholar 

  19. P. F. Smith, Rings characterized by their cyclic modules. Canad. J. Math.31, 93–111 (1979).

    Google Scholar 

  20. D. B. Webber, Ideals and modules of simple noetherian hereditary rings. J. Algebra16, 239–242 (1970).

    Google Scholar 

  21. R. Wisbauer, Modules locally of serial type. Per. Math. Acad. Sc. Hungar18, 39–52 (1987).

    Google Scholar 

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Research supported by the Alexander von Humboldt-Stiftung.

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van Huynh, D., Dân, P. On rings with restricted minimum condition. Arch. Math 51, 313–326 (1988). https://doi.org/10.1007/BF01194021

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