Kitajski izrek o ostankih

diplomsko delo

Nataša Plavčak (Author), Dominik Benkovič (Mentor)

Abstract

V diplomskem delu je predstavljen kitajski izrek o ostankih; najprej v teoriji števil in nato v splošnih kolobarjih. Na začetku je na kratko predstavljena zgodovina kitajskega izreka o ostankih. Sledi kitajski izrek o ostankih v teoriji števil in primer. V nadaljevanju je podrobneje opisana struktura kolobarjev. Predstavljeni so ideali in homomorfizmi kolobarjev ter izreki o izomorfizmih. Vse to je potrebno za razumevanje osrednjega dela diplome - kitajskega izreka o ostankih v splošnih kolobarjih. Na koncu je predstavljen subdirektni produkt kolobarjev, kjer imata pomembno vlogo prakolobar in pol prakolobar.

Keywords

matematika;kitajski izrek;ostanki;kolobarji;ideal;homomorfizem;direktni produkt;subdirektni produkt;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Plavčak]
UDC:	51(043.2)
COBISS:	18777864
Views:	2447
Downloads:	324
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	CHINESE REMAINDER THEOREM
Secondary abstract:	In this graduation thesis the Chinese remainder theorem is considered. First in the number theory and then in the ring theory. At the beginning we present the history of the Chinese remainder theorem. Then Chinese remainder theorem in the number theory is studied. Next, we turn our attention to the structure of rings. We also study ideals and homomorphisms of rings and we present theorems on isomorphisms. The main part of the thesis is devoted to the Chinese remainder theorem in the ring theory. At the end we introduce subdirect product of rings, where prime rings and semiprime rings have an important role.
Secondary keywords:	Chinese remainder theorem;ring;ideal;homomorphism;direct product;subdirect product.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	44 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19649