MODUL τ[M]-INJEKTIVE

Suprapto, Suprapto ( SMP 1 Banguntapan, Bantul, Yogyakarta Mahasiswa S3 Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Gadjah Mada, Yogyakarta)
Wahyuni, Sri ( Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Gadjah Mada, Yogyakarta)
Wijayanti, Indah Emilia ( Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Gadjah Mada, Yogyakarta)
Irawati, Irawati ( Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Institut Teknologi Bandung)

Journal of Mathematics and Mathematics Education
Vol 1, No 2 (2011): Journal of Mathematics and Mathematics Education

Abstract Let  R be a ring with unit and let  N be a left R-module. Then N is said linearly independent to  R (or N is R-linearly independent) if there is monomorphisma  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 is  M-linearly independent. The set of modules M-sublinearly independent denoted by  Can be shown easily that  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  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  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. Key words : Q ()-projective, P ()-injective.