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Some examples of right self-injective rings which are not left self-injective


Author: F. L. Sandomierski
Journal: Proc. Amer. Math. Soc. 26 (1970), 244-245
MSC: Primary 16.90
DOI: https://doi.org/10.1090/S0002-9939-1970-0265414-2
MathSciNet review: 0265414
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Abstract: Endomorphism rings of nonfinitely generated free right $ R$-modules over a quasi-Frobenius ring $ R$ are right self-injective but not left self-injective.


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

  • [1] G. Azumaya, Completely faithful modules and self-injective rings, Nagoya Math. J. 27 (1966), 697-708. MR 35 #4253. MR 0213389 (35:4253)
  • [2] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 17, 1040. MR 0077480 (17:1040e)
  • [3] C. Faith, Rings with ascending condition on annihilators, Nagoya Math. J. 27 (1966), 179-191. MR 33 #1328. MR 0193107 (33:1328)
  • [4] B. Osofsky, Cyclic injective modules of full linear rings, Proc. Amer. Math. Soc. 17 (1966), 247-253. MR 32 #7604. MR 0190190 (32:7604)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0265414-2
Keywords: Self-injective ring, quasi-Frobenius ring
Article copyright: © Copyright 1970 American Mathematical Society

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