Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/3781 2023 2023 Ministry of Education, Resafa, Iraq Hassan Hassan The main aim of this paper is extend the notion of S-extending fz-modules into LS-extending fz-modules and study this new notion. This lead us introduce and study other notions such as: purely semisimple, purely extending and purely y-extending fz-modules. Moreover, the relationships LS-extending fz-module with the various types. 2025 2025 12 20 10.54216/PMTCS.050102 https://www.americaspg.com/articleinfo/40/show/3781