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master's thesis
Komutativni prsteni i moduli
Osijek: Josip Juraj Strossmayer University of Osijek, Faculty of Applied Mathematics and Informatics, 2023. urn:nbn:hr:126:333655
Gavran, David
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Gavran, D. (2023). Komutativni prsteni i moduli (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:333655

Gavran, David. "Komutativni prsteni i moduli." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:333655

Gavran, David. "Komutativni prsteni i moduli." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:333655

Gavran, D. (2023). 'Komutativni prsteni i moduli', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 17 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:333655

Gavran D. Komutativni prsteni i moduli [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 November 17] Available at: https://urn.nsk.hr/urn:nbn:hr:126:333655

D. Gavran, "Komutativni prsteni i moduli", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:333655

Metadata
TitleKomutativni prsteni i moduli
Title (english)Commutative Rings And Modules
AuthorDavid Gavran
MentorIvan Matić (mentor)
Committee memberTomislav Marošević (predsjednik povjerenstva)
Committee memberIvan Matić (član povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-09-18, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom diplomskom radu napravljen je koncpet komuntativnih prstenova i modula. Nakon definiranja osnovnih pojmova i teorema iz teorije prstenova, baziramo se na komutativne prstenove i module. Upoznali smo se s uvjetima lanaca, primarnih idealima, primarnom dekompozicijom, Noetherinim prstenovima, proširenja prstenova te Dedekindovim domenama. Naveli smo važne teoreme algebre kao što su Krullov teorem, Hilbertov teorem o bazi, teorem koji povezuje pojmove Dedekindove domene, invertibilnih ideala, projektivnih ideala te Noetherinih prstenova. Upoznali smo se s pojmovima normalnog niza, kompozicionog niza, izoliranog ideala, anhilatora i prstena diskretne valuacije.
Abstract (english)
In this master’s thesis, a concept of commutative rings and modules is developed. After defining the basic concepts and theorems from ring theory, the focus shifts to commutative rings and modules. We become acquainted with chain conditions, primary ideals, primary decomposition, Noetherian rings, ring extensions, and Dedekind domains. Important algebraic theorems are stated, such as Krull’s theorem, Hilbert’s basis theorem, and a theorem connecting the concepts of Dedekind domains, invertible ideals, projective ideals, and Noetherian rings. We familiarize ourselves with the notions of a normal sequence, a composition series, an isolated ideal, an annihilator, and a ring of discrete valuation
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:333655
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-09-19 11:04:05