Semi-Simplicity Relative to Kernel Functors
Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1405-1411
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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.
Rubin, Robert A. Semi-Simplicity Relative to Kernel Functors. Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1405-1411. doi: 10.4153/CJM-1974-134-2
@article{10_4153_CJM_1974_134_2,
author = {Rubin, Robert A.},
title = {Semi-Simplicity {Relative} to {Kernel} {Functors}},
journal = {Canadian journal of mathematics},
pages = {1405--1411},
year = {1974},
volume = {26},
number = {6},
doi = {10.4153/CJM-1974-134-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-134-2/}
}
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