Path: Top -> Journal -> Jurnal Internasional -> Fuzzy Information and Engineering -> 2019 -> Volume 11, Issue 2
An Investigation of ℱ-Closure of Fuzzy Submodules of a Module
Oleh : Ujwal Medhi, Helen K. Saikia & Bijan Davvaz, Fuzzy Information and Engineering
Dibuat : 2021-08-26, dengan 0 file
Keyword : Fuzzy submodule, fuzzy closure, fuzzy torsion
Url : http://www.tandfonline.com/doi/full/10.1080/16168658.2021.1886820
Sumber pengambilan dokumen : Web
In this paper we introduce the notion of F -closure of fuzzy submodules of a module M. Our attempt is to investigate various characteristics of such F -closures. If F is a non- empty set of fuzzy left ideals of R and μ is a fuzzy submodule of M then the F-closure of μ is denoted by ClMF(μ). If F is weak closed under intersection then (1) F-closure of μ exhibits the submodule character, (2) the intersection of F closures of two fuzzy submodules equals the F -closure of intersection of the fuzzy submodules. If F is weak closed under intersection then the submodule property of F -closure implies that F is left closed. Moreover, if F is inductive then F is a topological filter if and only if F is a fuzzy submodule of M.
Deskripsi Alternatif :In this paper we introduce the notion of F -closure of fuzzy submodules of a module M. Our attempt is to investigate various characteristics of such F -closures. If F is a non- empty set of fuzzy left ideals of R and μ is a fuzzy submodule of M then the F-closure of μ is denoted by ClMF(μ). If F is weak closed under intersection then (1) F-closure of μ exhibits the submodule character, (2) the intersection of F closures of two fuzzy submodules equals the F -closure of intersection of the fuzzy submodules. If F is weak closed under intersection then the submodule property of F -closure implies that F is left closed. Moreover, if F is inductive then F is a topological filter if and only if F is a fuzzy submodule of M.
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