JP Journal of Algebra, Number Theory and Applications
Volume 40, Issue 1, Pages 91 - 112
(February 2018) http://dx.doi.org/10.17654/NT040010091 |
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T-SMALL SUBMODULES WITH RESPECT TO AN ARBITRARY SUBMODULE
Sukit Sangwirotjanapat and Sajee Pianskool
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Abstract: From the notion of small submodules, for submodules Tand of an R-module M, we define T-small submodules with respect to a submodule of a module M, where We show that T-small submodules with respect to are a generalization of small submodules. Moreover, we define the T-radical with respect to denoted by and show that where is a T-small submodule with respect to in some conditions. In addition, for any submodule Nof with we obtain the result that Finally, we extend the notion of covers to the notion of T-covers with respect to and some results are presented. |
Keywords and phrases: T-small submodules with respect to a submodule, T-radicals with respect to a submodule, T-covers with respect to a submodule, small submodules. |
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