Injective cogenerator rings and a theorem of Tachikawa. II
Abstract: The main theorem states that a right injective cogenerator ring R has strongly bounded basic ring , that is, every onesided ideal of contains an ideal . 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') is strongly right bounded and has finite left socle.
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