Rings whose cyclic modules are injective or projective
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- by S. C. Geol, S. K. Jain and Surjeet Singh PDF
- Proc. Amer. Math. Soc. 53 (1975), 16-18 Request permission
Abstract:
The object of this paper is to prove Theorem. For a ring $R$ the following are equivalent: (i) Every cyclic right $R$-module is injective or projective. (ii) $R = S \oplus T$ where $S$ is semisimple artinian and $T$ is a simple right semihereditary right Öre-domain whose every proper cyclic right module is injective.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, When are proper cyclics injective?, Pacific J. Math. 45 (1973), 97–112. MR 320069, DOI 10.2140/pjm.1973.45.97
- B. L. Osofsky, Noninjective cyclic modules, Proc. Amer. Math. Soc. 19 (1968), 1383–1384. MR 231857, DOI 10.1090/S0002-9939-1968-0231857-7
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 16-18
- MSC: Primary 16A52
- DOI: https://doi.org/10.1090/S0002-9939-1975-0382349-X
- MathSciNet review: 0382349