Nonsingular modules and 𝑅-homogeneous maps

Albrecht, Ulrich; Hausen, Jutta

doi:10.1090/S0002-9939-1995-1254828-7

Nonsingular modules and $R$-homogeneous maps
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by Ulrich Albrecht and Jutta Hausen

Proc. Amer. Math. Soc. 123 (1995), 2381-2389

DOI: https://doi.org/10.1090/S0002-9939-1995-1254828-7

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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.

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