The finite intersection property on annihilator right ideals
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- by J. M. Zelmanowitz PDF
- Proc. Amer. Math. Soc. 57 (1976), 213-216 Request permission
Abstract:
In this article the finite intersection property on annihilator right ideals will be shown to be an adequate substitute for more stringent chain conditions on such ideals. One application of the investigation will produce a new characterization of orders in semisimple artinian rings, another will generate new classes of absolutely torsion-free rings.References
- Nathan Divinsky, Rings and radicals, Mathematical Expositions, No. 14, University of Toronto Press, Toronto, Ont., 1965. MR 0197489
- A. W. Goldie, Semi-prime rings with maximum condition, Proc. London Math. Soc. (3) 10 (1960), 201–220. MR 111766, DOI 10.1112/plms/s3-10.1.201
- I. N. Herstein and L. Small, Nil rings satisfying certain chain conditions, Canadian J. Math. 16 (1964), 771–776. MR 166220, DOI 10.4153/CJM-1964-074-0
- Robert A. Rubin, Absolutely torsion-free rings, Bull. Amer. Math. Soc. 78 (1972), 854–856. MR 299635, DOI 10.1090/S0002-9904-1972-13060-X
- Jorge Viola-Prioli, On absolutely torsion-free rings, Pacific J. Math. 56 (1975), no. 1, 275–283. MR 379560
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 213-216
- MSC: Primary 16A34
- DOI: https://doi.org/10.1090/S0002-9939-1976-0419512-6
- MathSciNet review: 0419512