Abstract
Prime submodule is the abstraction to module theory of prime ideal in ring theory. A proper submodule N of an R-module M is called prime submodule if for all r in R and m in M such that rm in N implies r in (N:M) or m in N. Prime submodule also generalized into weakly prime submodule and almost prime submodule. This study deal with particular cases of both of them in Z-module M_2x2(Z_9), the three submodules are equivalent in case of non-zero submodule.
Highlights
Prime submodule is the abstraction to module theory of prime ideal
Prime submodule also generalized into weakly prime submodule
the three submodules are equivalent in case of non-zero submodule
Summary
Pada ‐modul ( ), submodul prima dapat dikarakterisasi sesuai teorema berikut. . Submodul adalah submodul prima dari ( ) jika dan hanya jika submodul berbentuk. Akibatnya untuk semua , sehingga diperoleh atau untuk semua. Definisi ini submodul prima kemudian diperlemah Hadi yang kemudian dinamakan submodul prima lemah. Submodul prima lemah didefinisikan oleh Hadi sebagai berikut. Dari definisi jelas submodul nol pasti merupakan submodul prima lemah. Berdasarkan definisi juga, submodul prima pasti merupakan submodul prima lemah, tapi tidak sebaliknya. {(̅̅ ̅̅)} adalah contoh submodul prima lemah, tapi bukan submodul prima. Hal ini (̅̅ ̅̅) (̅̅ ̅̅) tidak berakibat atau (̅̅ ̅̅) {(̅̅ ̅̅)}
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
