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Indah Emilia Wijayanti
Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Gadjah Mada, Yogyakarta
Education Mathematics

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MODUL τ[M]-INJEKTIVE Suprapto Suprapto; Sri Wahyuni; Indah Emilia Wijayanti; Irawati Irawati
Journal of Mathematics and Mathematics Education Vol 1, No 2 (2011): Journal of Mathematics and Mathematics Education
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v1i2.9934

Abstract

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.
Co-Authors Irawati Irawati Sri Wahyuni Suprapto Suprapto