Regular and Baer rings
HTML articles powered by AMS MathViewer
- by K. M. Rangaswamy
- Proc. Amer. Math. Soc. 42 (1974), 354-358
- DOI: https://doi.org/10.1090/S0002-9939-1974-0340326-8
- PDF | Request permission
Abstract:
The (von Neumann) regular Baer rings representable as the full ring $E(G)$ of all endomorphisms of an abelian group G are characterized. It is also shown that a countable regular Baer ring is Artinian semisimple.References
- L. Fuchs, Abelian groups, International Series of Monographs on Pure and Applied Mathematics, Pergamon Press, New York-Oxford-London-Paris, 1960. MR 0111783
- László Fuchs and K. M. Rangaswamy, On generalized regular rings, Math. Z. 107 (1968), 71–81. MR 233850, DOI 10.1007/BF01111051
- Irving Kaplansky, Rings of operators, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0244778
- R. S. Pierce, Modules over commutative regular rings, Memoirs of the American Mathematical Society, No. 70, American Mathematical Society, Providence, R.I., 1967. MR 0217056
- K. M. Rangaswamy, Abelian groups with endomorphic images of special types, J. Algebra 6 (1967), 271–280. MR 217180, DOI 10.1016/0021-8693(67)90082-8
- K. M. Rangaswamy, Representing Baer rings as endomorphism rings, Math. Ann. 190 (1970/71), 167–176. MR 271222, DOI 10.1007/BF01431499
- Yuzo Utumi, On continuous regular rings and semi-simple self injective rings, Canadian J. Math. 12 (1960), 597–605. MR 117250, DOI 10.4153/CJM-1960-053-9
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 354-358
- MSC: Primary 16A34
- DOI: https://doi.org/10.1090/S0002-9939-1974-0340326-8
- MathSciNet review: 0340326