MODUL Ï[M]-INJEKTIVE - Suprapto, Suprapto; Wahyuni, Sri; Wijayanti, Indah Emilia; Irawati, Irawati (Journal of Mathematics and Mathematics Education, 2011)
AbstractÂ LetÂ R be a ring with unit and letÂ N be a left R-module. Then N is said linearly independent toÂ R (or N is R-linearly independent) if there is monomorphisma Â By the definition of R-linearly independent, we may be able to generalize linearly independent relative to the R-module M. Module N is said M-linearly independent if there is monomorphisma .The module Q is said M-sublinearly independent if Q is a factor module of modules which isÂ M-linearly independent. The set of modules M-sublinearly independent denoted by Â Can be shown easily that Â is a subcategory of the category R-Mod. Also it can be shown that the submodules, factor modules and external direct sum of modules in Â is also in the .The module Q is called P-injective if for any morphisma Q defined on L submodules of P can be extended to morphisma Q with , where Â is the natural inclusion mapping. The module Q is called -injective if Q is P-injective, for all modules P in .In this paper, we studiet the properties and characterization of -injective. Trait among others that the direct summand of a module that is -injective also -injective. A module is -injective if and only if the direct product of these modules also are -injective.Â Key words : Q ()-projective, P ()-injective.