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Kajian terhadap K-Aljabar

KamiL, Moh. Irfan (2016) Kajian terhadap K-Aljabar. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA:

K-Aljabar dibangun atas suatu grup dengan menggunakan operasi biner⊙ pada (G,*), sehingga untuk setiap x,y di G didefinisikanx⊙y=x*y^(-1) dan e adalah unsur identitas di G, (G,*,⊙,e)memenuhi aksioma-aksioma tertentu disebut K-aljabar. Dalam penelitian ini diperoleh sifat-sifat K-aljabar, K-sub aljabar dan K-homomorfisme, misalkan suatu himpunan bagian tidak kosong H dari K-aljabar (G,*,⊙,e) disebut K-sub aljabar jika:
1. e∈H
2. h_1⊙h_2∈H,∀ h_1,h_1∈H

Misalkan K_1 dan K_2 merupakan K-aljabar. Suatu pemetaan φ dari K_1 ke K_2, dinotasikan dengan φ:K_1→K_2, disebut K-homomorfisme jika ∀ x_1,y_1∈K_1 berlaku φ(x_1⊙y_1 )=φ(x_1 )⊙φ(y_1 ), dimana φ(x_1 ),φ(y_1 )∈K_2.

ENGLISH:

K-algebra is built on a group by using binary operations ⊙on (G,*), so that for every x,y in G defined x ⊙y=x* y^(-1)and e is the identity element in G, (G,*,⊙,e)satisfies certain axioms called K-algebra. In this research, the properties of K-algebra, K-sub algebra, and K-homomorphism, for example a non-empty subset H of K-algebra (G,*,⊙,e)is called K-sub algebra if:
1. e∈H
2. h_1⊙h_2∈H,∀h_1,h_1∈H

Like K_1and K_2 are K-algebra. A mapping φ ofK_1to K_2, denoted by φ:K_1→K_2called K-homomorphism if ∀〖 x〗_1,y_1∈K_1applied φ(x_1⊙y_1 )=φ(x_1 )⊙φ(y_1 ), where φ(x_1 ),φ(y_1 )∈K_2.

Item Type: Thesis (Undergraduate)
Supervisor: Alisah, Evawati and Rozi, Fachrur
Contributors:
ContributionNameEmail
UNSPECIFIEDAlisah, EvawatiUNSPECIFIED
UNSPECIFIEDRozi, FachrurUNSPECIFIED
Keywords: Grup; Subgrup; K-Aljabar; K-Subaljabar; K-Homomorfisme; Group; Subgroup; K-Algebra; K-Sub Algebra; K-Homomorphism
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: Kumala Inayati
Date Deposited: 03 Aug 2016 11:08
Last Modified: 03 Aug 2016 11:08
URI: http://etheses.uin-malang.ac.id/id/eprint/4050

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