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undergraduate thesis
Hilbertov teorem o nulama
2023. urn:nbn:hr:126:447661
Sesar, Katarina
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Cite this document

Sesar, K. (2023). Hilbertov teorem o nulama (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:447661

Sesar, Katarina. "Hilbertov teorem o nulama." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:447661

Sesar, Katarina. "Hilbertov teorem o nulama." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:447661

Sesar, K. (2023). 'Hilbertov teorem o nulama', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 20 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:447661

Sesar K. Hilbertov teorem o nulama [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 November 20] Available at: https://urn.nsk.hr/urn:nbn:hr:126:447661

K. Sesar, "Hilbertov teorem o nulama", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:447661

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Metadata
TitleHilbertov teorem o nulama
Title (english)Hilbert's Nulls Theorem
AuthorKatarina Sesar
MentorIvan Matić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
Teme istražene u ovom radu spadaju u domenu komutativne algebre, obuhvaćajući i aspekte homološke algebre. Komutativna algebra čvrsto je povezana s algebarskom geometrijom, što predstavlja motivaciju za razvoj određenih koncepata unutar komutativne algebre. Osim toga, ovo je područje gdje se rezultati dobiveni proučavanjem tih koncepata mogu primijeniti u praksi. Iako su odnosi između geometrijskih objekata i matematičkih jednadžbi koje ih opisuju proučavani tijekom stoljeća, specifična povezanost između ovih dvaju područja nije bila potpuno jasna sve do sredine 19. stoljeća. U tom vremenskom razdoblju, David Hilbert je igrao ključnu ulogu svojim rezultatima, uključujući teorem o bazi, teorem o nulama, koncept polinomijalne strukture poznate kao Hilbertova funkcija i teorem o sizigiji. Ovi rezultati su postavili temelje komutativne algebre. Ovaj rad započinje analizom afinih algebarskih skupova, a zatim se bavi idealima, s posebnim fokusom na koordinatne prstene, k-algebre konačnog tipa i maksimalne ideale. Završno poglavlje istražuje temu "malog" i "velikog" Hilbertovog teorema o nulama te se bavi njihovim aspektima.
Abstract (english)
The topics covered in this text belong to the commutative algebra domain, including homological algebra elements. Commutative algebra is closely linked to algebraic geometry, which serves as motivation for the development of certain concepts within commutative algebra.Moreover, this is an area where results obtained by studying these concepts can be practically applied. Although the relationship between geometric objects and the mathematical equations that describe them has been studied for centuries, the specific connection between these two fields discussed here was not fully recognized until the mid-nineteenth century. During that period, David Hilbert’s results, including the basis theorem, the nullstellensatz, the polynomial structure known as Hilbert’s function, and the syzygy theorem, played a crucial role in laying the foundations of commutative algebra. This paper begins with an analysis of affine algebraic sets, followed by a discussion of ideals, with a particular focus on coordinate rings, finite-type k-algebras, and maximal ideals. The final chapter explores the topic of the "small" and "big" Hilbert nullstellensatz theorems and delves into their aspects.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:447661
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-10-06 10:23:03