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Proceedings of the American Mathematical Society

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

 

 

Injective cogenerator rings and a theorem of Tachikawa. II


Author: Carl Faith
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0429990-5
Article copyright: © Copyright 1977 American Mathematical Society