JP Journal of Algebra, Number Theory and Applications
Volume 42, Issue 2, Pages 171 - 187
(May 2019) http://dx.doi.org/10.17654/NT042020171 |
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ON THE UPPER NIL RADICAL FOR R-MODULES
N. J. Groenewald
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Abstract: Let M be a right R-module. In this paper a generalization of the notion of an s-system of rings to modules is given. Let N be a fully invariant submodule of M. Define every s-system containing m meets
It is shown that is equal to the intersection of all s-prime submodules of M containing N. We define This is called (Kothe’s) upper nil radical of M. We show that if M is a quasi-projective and finitely generated right R-module which is a self-generator, then is the sum of all fully invariant nil submodules of M. Finally we introduce the notion of NI-modules and NI submodules. |
Keywords and phrases: s-prime modules, upper nil radical, nil submodules, s-systems of modules.
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