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master's thesis
Osnovne algebarske strukture i proširenja polja
2024. urn:nbn:hr:126:554575
Babok, Ema
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Babok, E. (2024). Osnovne algebarske strukture i proširenja polja (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:126:554575

Babok, Ema. "Osnovne algebarske strukture i proširenja polja." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:554575

Babok, Ema. "Osnovne algebarske strukture i proširenja polja." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:554575

Babok, E. (2024). 'Osnovne algebarske strukture i proširenja polja', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 10 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:554575

Babok E. Osnovne algebarske strukture i proširenja polja [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 November 10] Available at: https://urn.nsk.hr/urn:nbn:hr:126:554575

E. Babok, "Osnovne algebarske strukture i proširenja polja", 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:126:554575

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Metadata
TitleOsnovne algebarske strukture i proširenja polja
Title (english)Basic Algebraic Structures And Field Extensions
AuthorEma Babok
MentorIvan Soldo (mentor)
Committee memberMirela Jukić Bokun (predsjednik povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
Committee memberLjiljana Primorac Gajčić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-10-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom radu proučavali smo osnovne algebarske strukture i kvadratna proširenja polja racionalnih brojeva. Počevši od osnovnih definicija i pojmova iz algebre, istražujemo kako se formiraju proširenja polja, s posebnim naglaskom na kvadratna proširenja. Nakon što smo konstruirali polje \(\mathbb{Q}( \sqrt{d})\) , definirali smo pojmove algebarskog broja i algebarskog cijelog broja. Daljnje analize uključuju primjere kvadratnih proširenja i njihovu primjenu u teoriji brojeva. Rad naglašava važnost kvadratnih proširenja u razumijevanju dubljih algebarskih struktura i njihovih svojstava.
Abstract (english)
In this final paper, we consider basic algebraic structures and quadratic extensions of rational numbers. Starting from basic definitions and concepts from algebra, we explore how field extensions are formed, with a particular emphasis on quadratic extensions. After constructing the field \(\mathbb{Q}( \sqrt{d})\), we define the concepts of algebraic numbers and algebraic integers, highlighting their key characteristics. Further analysis includes examples of quadratic extensions and their applications in number theory. We also examine how algebraic integers can serve as a foundation for studying algebraic structures within these extensions. In the context of these definitions, we particularly focus on how the solutions to quadratic equations can be interpreted within the extended fields. Finally, the thesis emphasizes the importance of quadratic extensions in understanding deeper algebraic structures and their properties.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:554575
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 on2024-11-04 12:10:15