Z-small critically compressible modules

For an R-module (R – mod) C and a commutative ring (with identity) R, we introduce the notion Z-Small critically compressible modules (An R-mod C is Z-small Critically compressible (ZSC – C) where C may not embedded, in proper quotient modules C ⁄ N with 0 ≠ N ≪Z C) as a generalization of Small critically compressible. We also provide the relationship between Z-small monoforms and Z-critically compressible modules in which the module is Z-small compressible.