Jordan-Hölderjev izrek

diplomsko delo

Ana Skok (Author), Dominik Benkovič (Mentor)

Abstract

V diplomskem delu je predstavljen Jordan-Hölderjev izrek na strukturi modulov. Na začetku so na kratko predstavljeni osnovni pojmi kolobarjev, idealov in modulov. Nato se seznanimo tudi z verižnimi pogoji, eksaktnimi zaporedji in kompozicijskimi vrstami, ki so potrebne za razumevanje celotnega diplomskega dela. Na koncu je predstavljen Jordan-Hölderjev izrek, ki ga dokažemo na dva različna načina. Pri prvem načinu si pomagamo s pomočjo pojma dolžina modula, medtem ko se pri drugem načinu dokazovanja opremo na Schreierjev izrek.

Keywords

diplomska dela;matematika;kolobar;modul;verižni pogoj;kompozicijska vrsta;

Data

Language:	Slovenian
Year of publishing:	2012
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[A. Skok]
UDC:	51(043.2)
COBISS:	19321864
Views:	1331
Downloads:	108
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	JORDAN-HÖLDER THEOREM
Secondary abstract:	In graduation thesis the Jordan-Hölders theorem on modules is presented. At the begining we introduce the basics of rings, modules and ideals. Next we consider the chain conditions, exact sequence and composition series, which are nessesery to understand the hole thesis. In the end part of the thesis we present the Jordan-Hölders theorem, which we can prove on two different ways. In the first way we help ourselves with the definition of length, and in the second way we depend on Schreiers theorem.
Secondary keywords:	ring;module;chain condition;exact sequence;composition series;the Jordan - Hölder theorem;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	40 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	1025965