On simple injective rings
HTML articles powered by AMS MathViewer
- by Sigurd Elliger PDF
- Proc. Amer. Math. Soc. 40 (1973), 93-94 Request permission
Abstract:
It is proved that a simple ring which is injective on both sides must be artinian. This answers a question asked by C. Faith in the negative.References
- Carl Faith, Lectures on injective modules and quotient rings, Lecture Notes in Mathematics, No. 49, Springer-Verlag, Berlin-New York, 1967. MR 0227206
- N. Jacobson, Some remarks on one-sided inverses, Proc. Amer. Math. Soc. 1 (1950), 352–355. MR 36223, DOI 10.1090/S0002-9939-1950-0036223-1
- Irving Kaplansky, Topological representation of algebras. II, Trans. Amer. Math. Soc. 68 (1950), 62–75. MR 32612, DOI 10.1090/S0002-9947-1950-0032612-4 J.-E. Roos, Sur l’anneau maximal de fractions des AW*-algèbres et des anneaux de Baer, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), A120-A123. MR 39 #6093.
- Yuzo Utumi, On continuous rings and self injective rings, Trans. Amer. Math. Soc. 118 (1965), 158–173. MR 174592, DOI 10.1090/S0002-9947-1965-0174592-8
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 93-94
- MSC: Primary 16A52
- DOI: https://doi.org/10.1090/S0002-9939-1973-0320074-X
- MathSciNet review: 0320074