Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-14T05:09:25.442Z Has data issue: false hasContentIssue false
  • English
  • Français

Semi-Simplicity Relative to Kernel Functors

Published online by Cambridge University Press:  20 November 2018

Robert A. Rubin
Robert A. Rubin*
Affiliation:
College of Arts and Sciences, Pahlavi University, Shiraz, Iran
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Λ be a ring and σ a kernel functor (left exact preradical) on the category of left Λ-modules. A left Λ-module M is called σ-semi-simple if whenever N is a submodule of M with M/Nσ-torsion, N is a direct summand of M. In Section 1 we consider alternative characterizations and properties of σ-semi-simplicity for modules. In Section 2 conditions equivalent to the σ-semi-simplicity of the ring are obtained. Section 3 is devoted to the condition, which frequently arises in Section 2, that every σ-torsion module be semisimple.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1405 - 1411
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Goldman, O., Rings and modules of quotients, J. Algebra 13 (1969), 10–47.Google Scholar
2. Goldman, O., A Wedderburn-Artin-Jacobson structure theorem (to appear).Google Scholar
3. Goodearl, K. R., Singular torsion and the splitting properties (to appear).Google Scholar
4. Tsai, C. T., Infective modules, Queen's Papers on Pure and Applied Math. No. 6 (Queen's University, Kingston, Ontario).Google Scholar