Projective maximal right ideals of self-injective rings
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- by O. A. S. Karamzadeh PDF
- Proc. Amer. Math. Soc. 48 (1975), 286-288 Request permission
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.References
- Irving Kaplansky, Projective modules, Ann. of Math (2) 68 (1958), 372–377. MR 0100017, DOI 10.2307/1970252
- Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032
- B. L. Osofsky, Rings all of whose finitely generated modules are injective, Pacific J. Math. 14 (1964), 645–650. MR 161886 J. Von Neumann, On regular rings, Proc. Nat. Acad. Sci. U.S.A. 22 (1936), 707-713.
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 286-288
- DOI: https://doi.org/10.1090/S0002-9939-1975-0360705-3
- MathSciNet review: 0360705