Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

BACKGROUND Post-stroke subjects with hemiparesis typically utilize a reduced number of modules or co-excited muscles compared to non-impaired controls, with at least one module resembling the merging of two or more non-impaired modules. In non-impaired walking, each module has distinct contributions to important biomechanical functions, and thus different merged module combinations post-stroke ...

The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules.

Abstract The theory of R. Crowell on derived modules is approached within the non-commutative differential modules. We also seek analogies to cotangent complex from differentials in commutative ring setting. Finally, we give examples motivated Galois coverings curves.