aspg-24-3203-1791482227 20261008175707 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2024 9 1 Khaled Moaz University of Mosul, department of computer science and mathematics, Mosul, Iraq Let I be a right (left) ideal of a ring R, then R/I is a right (left) generalized m – flat module (GmF – module) if and only if for each a Î I , there exists b Î I and a fixed positive integer m such that style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-fareast-font-family:Calibri;mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;font-style:italic'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>a style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>m style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>=b style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-fareast-font-family:Calibri;mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;font-style:italic'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>a style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>m style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>( style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-fareast-font-family:Calibri;mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;font-style:italic'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>a style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>m style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>= style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-fareast-font-family:Calibri;mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;font-style:italic'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>a style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>m style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi;color:black'>b) . In this paper, we study the characterization and properties this class of flat modules, and we give the relation between this class and generalized m- flat modules and m– regular rings, reduced rings, reversible rings and uniform rings. 2024 32 35 3203 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.090104 https://www.americaspg.com/journal/24/article/3203 https://www.americaspg.com/storage/71725489907.pdf