Nonsingular modules and $R$-homogeneous maps
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- by Ulrich Albrecht and Jutta Hausen PDF
- Proc. Amer. Math. Soc. 123 (1995), 2381-2389 Request permission
Abstract:
A non-singular R-module M is a ray for the class of all non-singular modules if every R-homogeneous map from M into a non-singular module is additive. Every essential extension of a non-singular locally cyclic module is a ray. We investigate the structure of rays, and determine those semi-prime Goldie-rings for which all non-singular modules are rays and those rings for which the only rays are essential extensions of locally cyclic modules.References
- P. Fuchs, C. J. Maxson, and G. Pilz, On rings for which homogeneous maps are linear, Proc. Amer. Math. Soc. 112 (1991), no. 1, 1–7. MR 1042265, DOI 10.1090/S0002-9939-1991-1042265-6
- K. R. Goodearl, Ring theory, Pure and Applied Mathematics, No. 33, Marcel Dekker, Inc., New York-Basel, 1976. Nonsingular rings and modules. MR 0429962 J. Hausen, Abelian groups whose semi-endomorphisms form a ring, Proceedings Abelian Groups and Modules (Curacao 1991).
- D. W. Sharpe and P. Vámos, Injective modules, Cambridge Tracts in Mathematics and Mathematical Physics, No. 62, Cambridge University Press, London-New York, 1972. MR 0360706
- Bo Stenström, Rings of quotients, Die Grundlehren der mathematischen Wissenschaften, Band 217, Springer-Verlag, New York-Heidelberg, 1975. An introduction to methods of ring theory. MR 0389953, DOI 10.1007/978-3-642-66066-5
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2381-2389
- MSC: Primary 16N60; Secondary 16Y30
- DOI: https://doi.org/10.1090/S0002-9939-1995-1254828-7
- MathSciNet review: 1254828