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On simple injective rings


Author: Sigurd Elliger
Journal: Proc. Amer. Math. Soc. 40 (1973), 93-94
MSC: Primary 16A52
DOI: https://doi.org/10.1090/S0002-9939-1973-0320074-X
MathSciNet review: 0320074
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Abstract: It is proved that a simple ring which is injective on both sides must be artinian. This answers a question asked by C. Faith in the negative.


References [Enhancements On Off] (What's this?)

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  • [2] N. Jacobson, Some remarks on one-sided inverses, Proc. Amer. Math. Soc. 1 (1950), 352-355. MR 12, 75. MR 0036223 (12:75e)
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  • [4] J.-E. Roos, Sur l'anneau maximal de fractions des AW*-algèbres et des anneaux de Baer, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), A120-A123. MR 39 #6093.
  • [5] Y. Utumi, On continuous rings and self injective rings, Trans. Amer. Math. Soc. 118 (1965), 158-173. MR 30 #4793. MR 0174592 (30:4793)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0320074-X
Article copyright: © Copyright 1973 American Mathematical Society

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