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Title:
KITAJSKI IZREK O OSTANKIH
Authors:
ID
Plavčak, Nataša
(
Author
)
ID
Benkovič, Dominik
(
Mentor
)
More about this mentor...
Files:
UNI_Plavcak_Natasa_2011.pdf
(236,99 KB)
MD5: AB74B765A8772D5A60F9E5BD1B02EC28
PID:
20.500.12556/dkum/6a9d4a2e-0af8-48b7-8841-4da04bc61fc0
Language:
Slovenian
Work type:
Undergraduate thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
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 tudi 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 polprakolobar.
Keywords:
kitajski izrek o ostankih
,
kolobar
,
ideal
,
homomorfizem
,
direktni produkt
,
subdirektni produkt
Place of publishing:
Maribor
Publisher:
[N. Plavčak]
Year of publishing:
2011
PID:
20.500.12556/DKUM-21224
UDC:
51(043.2)
COBISS.SI-ID:
18777864
NUK URN:
URN:SI:UM:DK:DRZWJDKQ
Publication date in DKUM:
23.11.2011
Views:
3266
Downloads:
384
Metadata:
Categories:
FNM
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Secondary language
Language:
English
Title:
CHINESE REMAINDER THEOREM
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.
Keywords:
Chinese remainder theorem
,
ring
,
ideal
,
homomorphism
,
direct product
,
subdirect product.
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