SIFAT RADIKAL ATAS SUBRING PEMBAGIAN SEJATI PADA SUBGRUP NORMAL SUATU GRUP PERKALIAN DARI RING PEMBAGIAN
In this thesis, we will discuss two important theorems about the division rings, that are Faith�s Theorem and Herstein�s Theorem. Let D be a division ring with center F and D a multiplicative group of D. Let D be a division ring with center F and D a multiplicative group of D. Faith�s Theorem...
Saved in:
| Main Authors: | , |
|---|---|
| 格式: | Theses and Dissertations NonPeerReviewed |
| 出版: |
[Yogyakarta] : Universitas Gadjah Mada
2014
|
| 主題: | |
| 在線閱讀: | https://repository.ugm.ac.id/134475/ http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=77088 |
| 標簽: |
添加標簽
沒有標簽, 成為第一個標記此記錄!
|
| 總結: | In this thesis, we will discuss two important theorems about the division
rings, that are Faith�s Theorem and Herstein�s Theorem. Let D be a division ring
with center F and D a multiplicative group of D. Let D be a division ring with
center F and D a multiplicative group of D. Faith�s Theorem states that if division
ring D is radical over proper subring division K of D, then D is field. If N is a
periodic subnormal subgroup of D, then N is contained in F. This is Herstein�s
Theorem. In addition, Herstein�s Lemma on D explains that if N is a subnormal
subgroup of D and radical over F, then there is M N normal subgroup of D
such that M is radical over F. Next, we will prove that Herstein�s Lemma and
Herstein�s Theorem are equivalence. The result to be obtained is generalization of
Faith�s and Herstein�s Theorem, that is if N is a normal subgroup of D which is
radical over proper subring division of D, then N is contained in F |
|---|