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Some classes of commutative rings with identity
Nikolina Kelava (2017)
University of Split
University of Split, Faculty of science
Department of Mathematics
Cite this document...

Kelava, N. (2017). Neke klase komutativnih prstena s jedinicom (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:771242

Kelava, Nikolina. "Neke klase komutativnih prstena s jedinicom." Master's thesis, University of Split, University of Split, Faculty of science, 2017. https://urn.nsk.hr/urn:nbn:hr:166:771242

Kelava, Nikolina. "Neke klase komutativnih prstena s jedinicom." Master's thesis, University of Split, University of Split, Faculty of science, 2017. https://urn.nsk.hr/urn:nbn:hr:166:771242

Kelava, N. (2017). 'Neke klase komutativnih prstena s jedinicom', Master's thesis, University of Split, University of Split, Faculty of science, accessed 22 March 2019, https://urn.nsk.hr/urn:nbn:hr:166:771242

Kelava N. Neke klase komutativnih prstena s jedinicom [Master's thesis]. Split: University of Split, University of Split, Faculty of science; 2017 [cited 2019 March 22] Available at: https://urn.nsk.hr/urn:nbn:hr:166:771242

N. Kelava, "Neke klase komutativnih prstena s jedinicom", Master's thesis, University of Split, University of Split, Faculty of science, Split, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:166:771242

Metadata
TitleNeke klase komutativnih prstena s jedinicom
Title (english)Some classes of commutative rings with identity
AuthorNikolina Kelava
MentorTanja Vučičić (mentor)
Committee memberTanja Vučičić (predsjednik povjerenstva)
Committee memberAnka Golemac (član povjerenstva)
Committee memberTea Martinić Bilać (član povjerenstva)
GranterUniversity of Split
University of Split, Faculty of science
(Department of Mathematics)
Split
Defense date and country2017-04-05, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu su opisane tri klase komutativnih prstena s jedinicom: euklidske domene, domene glavnih ideala i domene jedinstvene faktorizacije. Navedena su neka njihova zajednička, kao i specifična svojstva. Zajedničko svojstvo je npr. egzistencija najvećeg zajedničkog djelitelja. Specifično, u euklidskoj domeni postoji algoritam za određivanje najvećeg zajedničkog djelitelja. Za promatrane klase utvrđuje se međusobni odnos oblika niza skupovnih inkluzija: polja, euklidske domene, domene glavnih ideala, domene jedinstvene faktorizacije, integralne domene, gdje su sva sadržavanja prava. Naši važni primjeri su prsten cijelih brojeva Z i prsten polinoma F[x] s koecijentima iz danog polja F. U radu je pokazano da su neke općepoznate činjenice o svojstvima cijelih brojeva i polinoma iz Z[x] i Q[x] specijalni slučajevi tvrdnji koje vrijede u općenitijim prstenima.
Abstract (english)
In this thesis three classes of commutative rings with identity are described, that being Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains. Some of their common properties are given, as well as the specic ones. For instance, the existence of greatest common divisor is one of their common properties; specically, in Euclidean Domains g.c.d. can be computed algorithmically. The interrelation between classes proves to be a chain of inclusions elds, Euclidean Domains, Principal Ideal Domains, Unique Factorization Domains, integral domains, where all containments are proper. Our principal examples are the ring Z of integers and the polynomial rings F[x] with coe¢ cients in some eld F: It is shown that some well-known theorems on the integers Z and polynomials from Z[x] and Q[x] are special cases of results valid for more general rings.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:771242
Study programmeTitle: Matematika i informatika; smjerovi: nastavnički
Study programme type: sveučilišni
Study level: diplomski
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourcetext
File originBorn digital
Access conditionsRestricted access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2018-05-29 15:29:47