Some examples from infinite matrix rings
HTML articles powered by AMS MathViewer
- by Robert W. Miller and Darrel R. Turnidge PDF
- Proc. Amer. Math. Soc. 38 (1973), 65-67 Request permission
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
- Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488. MR 157984, DOI 10.1090/S0002-9947-1960-0157984-8
- Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
- Robert Gordon (ed.), Ring theory, Academic Press, New York-London, 1972. MR 0330129
- Robert W. Miller and Darrell R. Turnidge, Co-Artinian rings and Morita duality, Israel J. Math. 15 (1973), 12–26. MR 371949, DOI 10.1007/BF02771769
- F. L. Sandomierski, Linearly compact modules and local Morita duality, Ring theory (Proc. Conf., Park City, Utah, 1971) Academic Press, New York, 1972, pp. 333–346. MR 0344288
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 65-67
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310001-3
- MathSciNet review: 0310001