Generalization of K-Weak-S-Lifting Semimodules

Author : Moussa Sall, Landing Fall

Abstract : In this note we introduce the notions of k-weak-s-lifting(or wk-s-lifting for short) and k-weak-s- supplemented semimodules (or wk-s--supplemented semimodules for short) , and obtain some of their properties, characterizations, and decompositions. An R-semimodule M is called s-lifting if every subtractive subsemimodule N of M there exists a strong direct summand K of M such that and An R-semimodule M is called k-weak s-lifting (or wk-s-lifting for short) if every k-strongly k-semisimple subtractive subsemimodule N of M there exists a strong direct summand K of M such that and. An R-semimodule M is said to be a k-weak-s--supplemented semimodule, if for each strongly k semisimple subtractive submodule N of M there exists a strong direct summand K of M such that and. This allowed us to prove that not only every k-strongly k-semisimple semimodule is s-lifting if and only if it is wk-s-lifting but for any subtractive semimodule M such such that every supplement subsemimodule is fully invariant., M is wk-s--supplemented if and only if it is wk-s-lifting.

Keywords : Subtractive semimodule, s-lifting semimodule, k-weak-s-lifting semimodule and k-weak-s- supplemented.

Conference Name : International Conference on Algebraic Structures and Their Applications (ICASTA-26)

Conference Place : Marseille, France

Conference Date : 12th May 2026