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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Injective cogenerator rings and a theorem of Tachikawa. II
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by Carl Faith PDF
Proc. Amer. Math. Soc. 62 (1977), 15-18 Request permission

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.
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Additional 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