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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
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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

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