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Some examples from infinite matrix rings


Authors: Robert W. Miller and Darrel R. Turnidge
Journal: Proc. Amer. Math. Soc. 38 (1973), 65-67
DOI: https://doi.org/10.1090/S0002-9939-1973-0310001-3
MathSciNet review: 0310001
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Abstract | References | Additional Information

Abstract: Examples are given of the following: (1) an injective Noetherian right module which is not Artinian, (2) a linearly compact Noetherian right module over a right perfect ring which is not Artinian, and (3) a (linearly compact) Artinian left module over a right perfect ring which is not Noetherian. These examples answer questions posed by J. W. Fisher and F. L Sandomierski in the Proceedings of the Utah Conference on Ring Theory held in 1971.


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

  • [1] H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. MR 28 #1212. MR 0157984 (28:1212)
  • [2] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N.J., 1956. MR 17, 1040. MR 0077480 (17:1040e)
  • [3] R. Gordon (Editor), Ring theory, Academic Press, New York, 1972. MR 0330129 (48:8467)
  • [4] R. Miller and D. Turnidge, Co-Artinian rings and Morita duality, Israel J. Math. (to appear). MR 0371949 (51:8166)
  • [5] F. Sandomierski, ``Linearly compact modules and local Morita duality,'' in Ring theory, Academic Press, New York, 1972, pp. 333-346. MR 0344288 (49:9027)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310001-3
Keywords: Injective modules with chain conditions, linearly compact modules with chain conditions, perfect rings
Article copyright: © Copyright 1973 American Mathematical Society

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