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Baidowi Baidowi1
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Biochemistry, Genetics & Molecular Biology Chemistry Mathematics Physics

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KAJIAN KEINJEKTIFAN MODUL (MODUL INJEKTIF, MODUL INJEKTIF LEMAH, MODUL MININJEKTIF) Baidowi Baidowi1; Yunita Septriana Anwar
Jurnal Pijar Mipa Vol. 9 No. 1 (2014): Maret
Publisher : Department of Mathematics and Science Education, Faculty of Teacher Training and Education, University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (345.07 KB) | DOI: 10.29303/jpm.v9i1.43

Abstract

Abstrak. Diberikan  adalah -modul. Modul  dikatakan injektif jika untuk setiap monomorfisma   dan setiap homomorfisma  terdapat homomorfisma   sedemikian hingga . Modul  dikatakan injektif-lemah jika  adalah  -injektif lemah untuk setiap modul    yang dibangun berhingga. Sedangkan  dikatakan mininjektif jika untuk setiap homomorfisma dari  dengan  ideal sederhana dari , terdapat homomorfisma  sedemikian hingga . Kajian keinjektifan dalam tulisan ini meliputi modul injektif, modul injektif-lemah, dan modul mininjektif yang mengkaji karakterisasi dari masing-masing modul. Khusunya ketiganya memiliki karakterisasi yang khusus pada jumlahan tak berhingganya.Kata Kunci : Modul injektif, modul injektif-lemah, modul mininjektifAbstract. Let  be an -module. An -module  is called injective if for any monomrphism  and for any homomorphism  there exists a homomorphism  such that . We say that an -module  is weakly-injective if  is weakly -injective for every finitely generated module . An -module  is called mininjective if every homomorphism , there exists a homomorphism  such that , with  is simple ideal of . In this paper, we give some characterizations and properties of injective modules, weakly-injective modules, and mininjective modules. In particular, they have different characterizations for their infinite direct sum.Keywords : Injective modules, weakly-injective modules, mininjective modules
Co-Authors Yunita Septriana Anwar