Affiliations: [a] Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, India | [b] Department of Operations Research and Statistics, Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia | [c] College of Engineering, Yuan Ze University, Taoyuan City, Taiwan
Correspondence:
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Corresponding author: Abhishek Kumar Rath, Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh, India. E-mail: rathresearch495@gmail.com.
Abstract: In this article, we introduce the fuzzy generator and fuzzy cogenerator and investigate some of their properties. Necessary and sufficient conditions for a fuzzy module to become a fuzzy generator and sufficient conditions for a fuzzy module to become a fuzzy cogenerator have also been established. We also discuss the behavior of fuzzy modules of finitely generated modules. Further, we introduce fuzzy trace and fuzzy reject and establish some specific results. Finally, we define a faithful fuzzy module and weave this notion with the concepts of fuzzy generator and fuzzy cogenerator.
