Injective cogenerator rings and a theorem of Tachikawa. II
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- by Carl Faith
- Proc. Amer. Math. Soc. 62 (1977), 15-18
- DOI: https://doi.org/10.1090/S0002-9939-1977-0429990-5
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Abstract:
The main theorem states that a right injective cogenerator ring R has strongly bounded basic ring ${R_0}$, that is, every onesided ideal $\ne 0$ of ${R_0}$ contains an ideal $\ne 0$. A right injective cogenerator ring R is characterized by the condition: (1) R is semiperfect and right self-injective and (2) R has (finite) essential right socle. We show that (2) can be replaced by (2’) ${R_0}$ is strongly right bounded and has finite left socle.References
- Carl Faith, Injective cogenerator rings and a theorem of Tachikawa, Proc. Amer. Math. Soc. 60 (1976), 25–30 (1977). MR 417237, DOI 10.1090/S0002-9939-1976-0417237-4
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 15-18
- MSC: Primary 16A52
- DOI: https://doi.org/10.1090/S0002-9939-1977-0429990-5
- MathSciNet review: 0429990