JP Journal of Algebra, Number Theory and Applications
Volume 40, Issue 3, Pages 305 - 320
(June 2018) http://dx.doi.org/10.17654/NT040030305 |
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ON e-SMALL MONOFORM MODULES
Abdoul Djibril Diallo, Papa Cheikhou Diop and Mamadou Barry
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Abstract:
Let R be a commutative ring and M be a unital R-module. A submodule L of M is called an essential submodule of M, if for any nonzero submodule K of M. A submodule N of M is called an e-small submodule of M if, for any essential submodule L of M, implies An R-module M is called an e-small monoform if, for each nonzero submodule N of M and for each nonzero is e-small in N. In this paper, we introduce the concept of e-small monoform modules as a generalization of monoform modules, and give some of their properties, characterizations and examples.
On the other hand, we study the relations between e-small monoform modules and other related modules.
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Keywords and phrases: small submodules, e-small submodules, monoform modules, e-small monoform modules. |
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