Nerazcepni bikvadratni polinomi, ki so razcepni po poljubnem modulu p

diplomsko delo

Jasmina Kline (Author), Daniel Eremita (Mentor)

Abstract

V diplomskem delu je obravnavan problem razcepljenosti bikvadratnih polinomov s celoštevilskimi koeficienti. V prvem poglavju so predstavljeni pojmi in rezultati s področja teorije kongruenc, ki so potrebni za nadaljnjo obravnavo. V drugem poglavju so vpeljani pojmi in rezultati s področja polinomov z racionalnimi koeficienti, v tretjem poglavju pa polinomske kongruence na množici vseh polinomov s celoštevilskimi koeficienti. Osrednji del diplomskega dela je namenjen obravnavi bikvadratnih polinomov, ki so nerazcepni v Z[x], vendar so razcepni po modulu p za vsako praštevilo p. V zadnjem poglavju so obravnavani taki nerazcepni bikvadratni polinomi, ki so razcepni po modulu n za vsako naravno število n > 1.

Keywords

matematika;polinomi;bikvadratni polinomi;kongruenca;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2010
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[J. Kline]
UDC:	51(043.2)
COBISS:	17982984
Views:	1871
Downloads:	174
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	IRREDUCIBLE BIQUADRATIC POLYNOMALS WITH FACTORIZATIONS MODULO p
Secondary abstract:	The graduation thesis discusses a problem of irreducible biquadratic polynomials with integer coefficients. In the first chapter the theory of congruences is introduced. The second chapter is devoted to the theory of polynomials with rational coefficients. Next, we consider polynomial congruences on the set of all polynomials with integer coefficients. The main part of the thesis deals with biquadratic polynomials which are irreducible in Z[x], but reducible modulo p for every prime number p. In the last chapter we consider irreducible biquadratic polynomials that are reducible modulo n for every integer n > 1.
Secondary keywords:	biquadratic polynomial;congruence;polynomial;quadratic residue;Legendre symbol;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	IX, 49 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18912