SIFAT RADIKAL ATAS SUBRING PEMBAGIAN SEJATI PADA SUBGRUP NORMAL SUATU GRUP PERKALIAN DARI RING PEMBAGIAN; RADICAL OVER A PROPER DIVISION SUBRING ON NORMAL SUBGROUPS OF A MULTIPLICATIVE GROUP OF DIVISION RINGS

JULI LOISIANA BUTARBUTAR, Budi Surodjo

2014 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

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.

Kata Kunci : RADICAL OVER A PROPER DIVISION SUBRING, DIVISION RINGS