KAJIAN KEINJEKTIFAN MODUL (MODUL INJEKTIF, MODUL INJEKTIF LEMAH, MODUL MININJEKTIF)
DOI:
10.29303/jpm.v9i1.43Published:
2014-03-01Downloads
Abstract
Abstrak. Diberikan ÃÂ adalah -modul. Modul ÃÂ dikatakan injektif jika untuk setiap monomorfismaÃÂ ÃÂ dan setiap homomorfisma ÃÂ terdapat homomorfismaÃÂ ÃÂ sedemikian hingga . Modul ÃÂ dikatakan injektif-lemah jika ÃÂ adalahÃÂ -injektif lemah untuk setiap modulÃÂ ÃÂ yang dibangun berhingga. Sedangkan ÃÂ dikatakan mininjektif jika untuk setiap homomorfisma dari ÃÂ dengan ÃÂ ideal sederhana dari , terdapat homomorfisma ÃÂ 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 mininjektif
Abstract. Let ÃÂ be an -module. An -module ÃÂ is called injective if for any monomrphism ÃÂ and for any homomorphism ÃÂ there exists a homomorphism ÃÂ such that . We say that an -module ÃÂ is weakly-injective if ÃÂ is weakly -injective for every finitely generated module . An -module ÃÂ is called mininjective if every homomorphism , there exists a homomorphism ÃÂ such that , with ÃÂ 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 modulesLicense
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