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Proceedings of the American Mathematical Society

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

 

 

Projective maximal right ideals of self-injective rings


Author: O. A. S. Karamzadeh
Journal: Proc. Amer. Math. Soc. 48 (1975), 286-288
DOI: https://doi.org/10.1090/S0002-9939-1975-0360705-3
MathSciNet review: 0360705
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Abstract | References | Additional Information

Abstract: It is proved that a projective maximal right ideal $ M$ of a self-injective ring $ R$ is of the form $ M = eR + J(R)$. It is also shown that if every maximal right ideal of a self-injective ring $ R$ is projective, then $ R$ must be Artin semisimple.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0360705-3
Keywords: Self-injective ring, regular ring, essential submodule, singular submodule, semiperfect ring
Article copyright: © Copyright 1975 American Mathematical Society