JP Journal of Algebra, Number Theory and Applications
Volume 45, Issue 2, Pages 137 - 155
(February 2020) http://dx.doi.org/10.17654/NT045020137 |
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RINGS WHOSE CYCLIC MODULES ARE RADICAL LIFTING MODULES
Soumitra Das and Ardeline M. Buhphang
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Abstract: A right R-module M is called a radical lifting if for every submodule N of M, with there exists a module decomposition such that and is small in In this paper, we study sufficient conditions for a direct summand, factor module of a radical lifting module to be radical lifting. Thereafter, we study rings over which every cyclic right R-module is a radical lifting module. Examples are provided to illustrate the necessity and the sufficiency of the conditions in our result. We also provide examples to show that the class of rings all of whose cyclic right modules are radical lifting is not left-right symmetric. |
Keywords and phrases: supplemented modules, H-supplemented modules, ⊕-supplemented modules, lifting modules, radical lifting modules, semiperfect rings.
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