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master's thesis
Noetherini prsteni i moduli
2024. urn:nbn:hr:126:361599
Nuić, Mario
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Cite this document

Nuić, M. (2024). Noetherini 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:126:361599

Nuić, Mario. "Noetherini prsteni i moduli." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:361599

Nuić, Mario. "Noetherini prsteni i moduli." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:361599

Nuić, M. (2024). 'Noetherini prsteni i moduli', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 24 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:361599

Nuić M. Noetherini prsteni i moduli [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 December 24] Available at: https://urn.nsk.hr/urn:nbn:hr:126:361599

M. Nuić, "Noetherini prsteni i moduli", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:361599

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Metadata
TitleNoetherini prsteni i moduli
Title (english)Noetherian Rings And Modules
AuthorMario Nuić
MentorIvan Matić (mentor)
Committee memberMirela Jukić Bokun (predsjednik povjerenstva)
Committee memberIvan Matić (član povjerenstva)
Committee memberJelena Jankov Pavlović (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-10-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom diplomskom radu obrađuju se ključni pojmovi iz teorije Noetherinih prstena i modula. Nakon pregleda osnovnih kriterija i uvjeta za Noetherine prstene, analizirali smo pridružene proste ideale, odnosno proste ideale povezane s modulom, koji opisuju ključne elemente njegove strukture kroz dekompoziciju. Nakayamina lema kaže da u lokalnim Noetherinim prstenima injektivni moduli imaju posebnu strukturu koja ih čini projektivnima. Filtrirani i gradirani moduli omogućuju uvođenje dodatnih struktura koje pojednostavljuju analizu, a Hilbertov polinom služi za izračunavanje dimenzija tih struktura. Na kraju, obrađuju se nerazloživi moduli kao osnovni gradivni elementi.
Abstract (english)
This thesis addresses key concepts from the theory of Noetherian rings and modules. After reviewing the basic criteria and conditions for Noetherian rings, we analyzed associated primes, prime ideals related to a module, which describe key elements of its structure through decomposition. Nakayama’s lemma states that in local Noetherian rings, injective modules have a special structure that makes them projective. Filtered and graded modules allow the introduction of additional structures that simplify analysis, and the Hilbert polynomial is used to calculate the dimensions of these structures. Finally, indecomposable modules are discussed as fundamental building blocks.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:361599
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 on2024-10-29 10:52:35