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master's thesis
Moduli nad domenama glavnih ideala
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:130169
Hrvoj, Dora
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Hrvoj, D. (2020). Moduli nad domenama glavnih ideala (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:130169

Hrvoj, Dora. "Moduli nad domenama glavnih ideala." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:130169

Hrvoj, Dora. "Moduli nad domenama glavnih ideala." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:130169

Hrvoj, D. (2020). 'Moduli nad domenama glavnih ideala', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:130169

Hrvoj D. Moduli nad domenama glavnih ideala [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 May 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:130169

D. Hrvoj, "Moduli nad domenama glavnih ideala", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:130169

Metadata
TitleModuli nad domenama glavnih ideala
AuthorDora Hrvoj
MentorOzren Perše (mentor)
Committee memberOzren Perše (predsjednik povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
Committee memberPavle Pandžić (član povjerenstva)
Committee memberDamir Bakić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-02-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Glavni cilj ovog rada je proučiti pojam \(R\)-modula gdje je \(R\) domena glavnih ideala. Rad se sastoji od dvaju poglavlja. U prvom poglavlju predstavljaju se osnovne algebarske strukture, grupe i prstenovi te se pojašnjavaju moduli. U drugom poglavlju detaljnije se predstavljaju moduli nad domenama glavnih ideala. U ovom radu, glavni naglasak stavljen je na konačno generirane module čiji rezultati proizlaze iz generaliziranih tvrdnji o Abelovim grupama. Strukturne teoreme za konačne Abelove grupe generalizirat ćemo na module nad domenama glavnih ideala, iz čega zaključujemo da se ne generaliziraju samo teoremi već i dokazi.
Abstract (english)
The main objective of this paper is to study the notion of \(R\)-module where \(R\) is the principal ideal domain. This paper consists of two chapters, the first chapter presenting basic algebraic structures, groups and rings and explaining the modules. The second chapter presents the modules over principal ideal domain in more detail. The main emphasis of this paper is placed on the finitely generated modules whose results are derived from generalized statements about Abelian groups. We will generalize the structural theorems for finite Abelian groups to modules over principal ideal domain, from which we conclude that not only the theorems are generalized but also the proofs.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:130169
Study programmeTitle: Applied 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 on2020-07-23 10:44:58