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# Topic: Algebraic number

###### In the News (Wed 19 Jun 19)

 Algebraic Number Theory Archive   (Site not responding. Last check: 2007-10-20) This archive is for research in algebraic number theory and arithmetic geometry. math.NT/0310162: 11 Oct 2003, Algebraic cycles on Hilbert modular fourfolds and poles of L-functions, by Dinakar Ramakrishnan. ANT-0267: 27 Nov 2000, On an analogue for number fields of a conjecture of de Jong on F_q[[t]]-analytic extensions of function fields, by Gebhard Boeckle. front.math.ucdavis.edu /ANT   (12251 words)

 PlanetMath: algebraic number theory Algebraic number theory is the study of algebraic numbers, their properties and their applications. The main object of study in algebraic number theory is the number field. This is version 30 of algebraic number theory, born on 2005-03-15, modified 2006-03-07. planetmath.org /encyclopedia/AlgebraicNumberTheory.html   (953 words)

 Algebraic number - Wikipedia, the free encyclopedia Most complex numbers are transcendental, because the set of algebraic numbers is countable while the set of complex numbers, and therefore the set of transcendental numbers, is not (since the union of two countable sets is countable). Given an algebraic number, there is a monic polynomial of least degree that has the number as a root. An algebraic number of degree 1 is a rational number. en.wikipedia.org /wiki/Algebraic_number   (554 words)

 Algebraic number field - Wikipedia, the free encyclopedia In mathematics, an algebraic number field (or simply number field) is a finite-dimensional (and therefore algebraic) field extension of the rational numbers Q. The study of algebraic number fields, and these days also of infinite algebraic extensions of the rational number field, is the central topic of algebraic number theory. This situation changed with the discovery of p-adic numbers by Hensel in 1897; and now it is standard to consider all of the various possible embeddings of a number field F into its various topological completions at once. en.wikipedia.org /wiki/Algebraic_number_field   (2164 words)

 The Prime Glossary: algebraic number   (Site not responding. Last check: 2007-10-20) A real number is an algebraic number if it is a zero of a polynomial with integer coefficients; and its degree is the least of the degrees of the polynomials with it as a zero. For example, the rational number a/b (with a, b and non-zero integers) is an algebraic number of degree one, because it is a zero of bx-a. In fact, almost all real numbers are transcendental because the set of algebraic numbers is countable. primes.utm.edu /glossary/page.php?sort=AlgebraicNumber   (123 words)

 1.3.4 Algebraic Number Theory -- Dr S Howson -- 16 HT   (Site not responding. Last check: 2007-10-20) Algebraic number theory determines to what extent arithmetic in rings like Algebraic integers; existence and properties of an integral basis; examples, including quadratic and cyclotomic fields. Algebraic Number Theory, by I. Stewart and D. Tall, (Chapman and Hall) follows the course most closely and is a relatively easy read. www.maths.ox.ac.uk /current-students/undergraduates/handbooks-synopses/2004/html/sect-c-04/node15.html   (237 words)

 MIT OpenCourseWare | Mathematics | 18.786 Topics in Algebraic Number Theory, Spring 2006 | Home Some important properties of algebraic numbers follow from Minkowski's theorem: given a lattice in a Euclidean space, any bounded, convex, centrally symmetric region of large enough volume contains a nonzero lattice point. This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. ocw.mit.edu /OcwWeb/Mathematics/18-786Spring-2006/CourseHome/index.htm   (166 words)

 What's New in Mathematica 5: Other Functions: Algebraic Number Objects object contains the minimal polynomial of the algebraic number and the root number--an integer indicating which of the roots of the minimal polynomial the common algebraic number field containing {a, b, c}, which takes only a fraction of a second. Arithmetic within the common number field is much faster. www.wolfram.com /products/mathematica/newin5/numberobjects.html   (166 words)

 Algebra Worksheets: Fundamentals of Equations and Formulas! Arithmetic on left with equivalent algebra expression on the right Same as previous worksheet but has the answers and a box to fill in the missing number or unknown Some more difficult problems; Equivalent algebra is on the right www.edhelper.com /algebra.htm   (1712 words)

 Mathematical Subject Classification The MSC is broken down into over 5,000 two-, three-, and five-digit classfications, each corresponding to a discipline of mathematics (e.g., 11 = Number theory; 11B = Sequences and sets; 11B05 = Density, gaps, topology). The current classification system, 2000 Mathematics Subject Classification (MSC2000), is a revision of the 1991 Mathematics Subject Classification, which is the classification that has been used by MR and Zbl since the beginning of 1991. Category theory; homological algebra {For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology} www.ams.org /msc   (607 words)

 Algebraic Geometry and Number Theory with Magma A week-long conference on the Computer Algebra system Magma and its applications to computational algebraic geometry and number theory was held October 4 - 8, 2004. Talks describing significant applications of Magma to algebraic geometry or number theory. A number of short courses providing an introduction to the use of Magma in various branches of algebraic geometry and number theory will be presented. magma.maths.usyd.edu.au /ihp   (374 words)

 [No title] Galois groups of number fields generated by torsion points of elliptic curves On Galois groups of p-closed number fields with restricted ramification II On the maximal unramified p-extension of an algebraic number field www.mathi.uni-heidelberg.de /~wingberg/agwingberg/wingberg.html   (248 words)

 The distribution of the irreducibles in an algebraic number field   (Site not responding. Last check: 2007-10-20) The distribution of the irreducibles in an algebraic number field We study the distribution of principal ideals generated by irreducible elements in an algebraic number field. Download the article in PDF format (size 162 Kb) www.austms.org.au /Publ/JAustMS/V79P3/c97.html   (45 words)

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