Results 251 to 260 of about 10,885,302 (272)
Some of the next articles are maybe not open access.
On the question of the algebraic independence of algebraic powers of algebraic numbers
Mathematical Notes of the Academy of Sciences of the USSR, 1972We obtain results showing that transcendental numbers of the form αβ, wherea≠0, 1, β is irrational, anda and β are algebraic numbers, cannot be expressed algebraically in terms of two of the numbers. The proof is carried out by A. O. Gel'fond's method.
openaire +2 more sources
2011
This first chapter has essentially an algebraic flavor. The exercises use elementary properties of the complex numbers. A first definition of the exponential function is given, and we also meet Blaschke factors. These will appear in a number of other places in the book, and are key players in more advanced courses on complex analysis. Almost no methods
openaire +2 more sources
This first chapter has essentially an algebraic flavor. The exercises use elementary properties of the complex numbers. A first definition of the exponential function is given, and we also meet Blaschke factors. These will appear in a number of other places in the book, and are key players in more advanced courses on complex analysis. Almost no methods
openaire +2 more sources
A course in computational algebraic number theory
Graduate texts in mathematics, 1993H. Cohen
semanticscholar +1 more source
2011
Chapter 2 reviews basic ideas of natural, real, integer and rational number sets, and how they are manipulated arithmetically and algebraically. The chapter contains sections on axioms, expressions, equations and ordered pairs, and concludes with an introductory description of groups, abelian groups, rings and fields.
openaire +2 more sources
Chapter 2 reviews basic ideas of natural, real, integer and rational number sets, and how they are manipulated arithmetically and algebraically. The chapter contains sections on axioms, expressions, equations and ordered pairs, and concludes with an introductory description of groups, abelian groups, rings and fields.
openaire +2 more sources
2012
This chapter is an introduction to algebraic number fields, which arose from both a generalization of the arithmetic in ℤ and the necessity to solve certain Diophantine equations. After recalling basic concepts from algebra and providing some polynomial irreducibility tools, the ring of integers \(\mathcal {O}_{\mathbb {K}}\) of an algebraic number ...
openaire +2 more sources
This chapter is an introduction to algebraic number fields, which arose from both a generalization of the arithmetic in ℤ and the necessity to solve certain Diophantine equations. After recalling basic concepts from algebra and providing some polynomial irreducibility tools, the ring of integers \(\mathcal {O}_{\mathbb {K}}\) of an algebraic number ...
openaire +2 more sources
Conductor ideals of orders in algebraic number fields
, 2014G. Lettl, C. Prabpayak
semanticscholar +1 more source
Science, 1926