Fuzzy essential-small submodules and fuzzy small-essential submodules

Document Type : Research Paper

Authors

1 Department of Mathematics, Dr.Vitthalrao Vikhe Patil College of Engineering,Ahmednagar 414001, India

2 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India

Abstract

In this paper, we introduce the concepts of a fuzzy essential-small submodule and a fuzzy small-essential submodule of
a module. We investigate various properties of such fuzzy submodules. It is also shown that the Jacobson L-radical is the sum of all essential-small L-submodules of a module. We also prove that the L-socle is the intersection of all small-essential L-submodules of a module. 

Keywords

References

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Journal of Hyperstructures
Volume 9, Issue 2
December 2020
Pages 52-67

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