Izreki o ničlah

delo diplomskega seminarja

Jon Mikoš (Author), Jaka Cimprič (Mentor)

Abstract

Hilbertov izrek o ničlah tvori osnovo algebraične geometrije. V delu izpeljemo analogno trditev za realna števila – realni izrek o ničlah. Nato vpeljemo posplošitev pojma realnosti na nekomutativne kolobarje. Dokažemo korespondenco med ideali v kolobarju realnih polinomov in kolobarju kvaternionskih polinomskih funkcij. S tem rezultatom prevedemo kvaternionski izrek o ničlah na realnega. Na koncu podamo znane posplošitve in nadaljnje smeri obravnave.

Keywords

matematika;realna polja;realni izrek o ničlah;kvaternionski izrek o ničlah;kolobarji z involucijo;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[J. Mikoš]
UDC:	512
COBISS:	120961795
Views:	480
Downloads:	55
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Nullstellensätze
Secondary abstract:	Hilbert’s Nullstellensatz forms the basis of algebraic geometry. In this paper we derive an analogous statement over the field of real numbers – the real Nullstellensatz. After that we introduce a generalization of real rings to the noncommutative setting. We prove a correspondence of ideals in the ring of real polynomials with the ideals in the ring of quaternionic polynomial functions. With this result we reduce the quaternionic Nullstellensatz to the real one. Finally, we state known generalizations and some further courses of study.
Secondary keywords:	mathematics;real fields;real Nullstellensatz;quaternionic Nullstellensatz;rings with involution;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	37 str.
ID:	16439144