On some rings whose modules have maximal submodules
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- by V. P. Camillo PDF
- Proc. Amer. Math. Soc. 50 (1975), 97-100 Request permission
Abstract:
It is shown that a principal right ideal domain, having the property that every right $R$ module has a maximal submodule must be simple. Strong conditions satisfied by these rings are deduced giving evidence for the conjecture that they must be $V$-rings. We also generalize an example of Faith by showing that a subring of an infinite dimensional full linear ring, which contains the socle of that ring is never a left $V$-ring.References
- John H. Cozzens, Homological properties of the ring of differential polynomials, Bull. Amer. Math. Soc. 76 (1970), 75–79. MR 258886, DOI 10.1090/S0002-9904-1970-12370-9
- Carl Faith, Lectures on injective modules and quotient rings, Lecture Notes in Mathematics, No. 49, Springer-Verlag, Berlin-New York, 1967. MR 0227206
- L. A. Koĭfman, Rings over which each module has a maximal submodule, Mat. Zametki 7 (1970), 359–367 (Russian). MR 262303
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 97-100
- MSC: Primary 16A48
- DOI: https://doi.org/10.1090/S0002-9939-1975-0382343-9
- MathSciNet review: 0382343