Yonathan, Barry (2013) KELAS-KELAS RING DAN IMPLIKASINYA SERTA MODUL SEMI-KOMUTATIF DAN P.Q-BAER. S1 thesis, Universitas Pendidikan Indonesia.
Abstract
Suatu ring R disebut ring terreduksi jika a^2=0 mengakibatkan a=0 untuk setiap a∈R, suatu ring R disebut ring McCoy jika untuk setiap polinom tak nol f(x)=a_0+a_1 x+⋯+a_n x^n, dan g(x)=b_0+b_1 x+⋯+b_m x^m∈R[x], sedemikian sehingga f(x)g(x)=0, maka terdapat r,s≠0∈R, sedemikian sehingga f(x)r=0 dan s(g(x))=0. Suatu ring R disebut ring 2-primal jika berlaku P(R)=N(R). Kelas dari ketiga ring tersebut beserta kelas ring simetrik, kelas ring reversibel, kelas ring semi-komutatif, kelas ring abelian, dan kelas ring Dedekind finite, kelas ring Armendariz, dan kelas ring duo memiliki suatu hubungan implikasi yang secara keseluruhan dapat dinyatakan dalam suatu diagram. Suatu modul M atas ring R disebut modul semi-komutatif, jika untuk setiap a∈R, dan m∈M, sedemikian sehingga ma=0, maka mRa=0, dan suatu modul M atas ring R disebut modul P.Q-Baer jika untuk setiap m∈M, berlaku A(mR)=eR, untuk suatu idempoten e.
Kata kunci: ring terreduksi, ring McCoy, ring 2-primal, modul semi-komutatif, dan modul P.Q-Baer.
A ring R is said to be reduced if a^2=0 implies a=0 for every a∈R, a ring R is said to be McCoy if for every non-zero polynomial f(x)=a_0+a_1 x+⋯+a_n x^n, and g(x)=b_0+b_1 x+⋯+b_m x^m∈R[x] such that f(x)g(x)=0, then there exist r,s≠0∈R, such that f(x)r=0 and s(g(x))=0. A ring R is called 2-primal if N(R)=P(R). Each class of those rings with the classes of symmetric, reversible, semi-commutative, abelian, Dedekind finite, Armendariz, and duo rings may have some implicative relations which can be drawn as an implication chart. A module M over ring R is said to be semi-commutative if ma=0 implies mRa=0, for all m∈M and a∈R. A module M over ring R is said to be P.Q-Baer if A(mR)=eR, for all m∈M, and some idempoten e.
Keywords: reduced ring, McCoty ring, 2-primal ring, semi-commutative module, P.Q-Baer module.
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| Item Type: | Thesis (S1) |
|---|---|
| Subjects: | Universitas Pendidikan Indonesia > Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1 > Program Studi Pendidikan Matematika |
| Divisions: | Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Program Studi Matematika - S1 > Program Studi Pendidikan Matematika |
| Depositing User: | Riki N Library ICT |
| Date Deposited: | 27 Aug 2013 07:27 |
| Last Modified: | 27 Aug 2013 07:27 |
| URI: | http://repository.upi.edu/id/eprint/405 |
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