KAJIAN KEINJEKTIFAN MODUL (MODUL INJEKTIF, MODUL INJEKTIF LEMAH, MODUL MININJEKTIF)

Authors

Baidowi Baidowi1 , Yunita Septriana Anwar

DOI:

10.29303/jpm.v9i1.43

Published:

2014-03-01

Issue:

Vol. 9 No. 1 (2014): Maret

Articles

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How to Cite

Baidowi1, B., & Anwar, Y. S. (2014). KAJIAN KEINJEKTIFAN MODUL (MODUL INJEKTIF, MODUL INJEKTIF LEMAH, MODUL MININJEKTIF). Jurnal Pijar Mipa, 9(1). https://doi.org/10.29303/jpm.v9i1.43
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Abstract

Abstrak. Diberikan àadalah -modul. Modul àdikatakan injektif jika untuk setiap monomorfismaà àdan setiap homomorfisma àterdapat homomorfismaà àsedemikian hingga . Modul àdikatakan injektif-lemah jika àadalahà -injektif lemah untuk setiap modulà à yang dibangun berhingga. Sedangkan àdikatakan mininjektif jika untuk setiap homomorfisma dari àdengan àideal sederhana dari , terdapat homomorfisma àsedemikian 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 àbe an -module. An -module àis called injective if for any monomrphism àand for any homomorphism àthere exists a homomorphism àsuch that . We say that an -module àis weakly-injective if àis weakly -injective for every finitely generated module . An -module àis called mininjective if every homomorphism , there exists a homomorphism àsuch that , with àis 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

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