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Ring of integers
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21	A NON-FREE RELATIVE INTEGRAL EXTENSION KEITH CONRAD 1. Introduction The ring of integers of any algebraic number field is free as a Z-module. More precisely, if [K : Q] = n, then there are ω1 , . . . , ωn such that Add to Reading List Source URL: www.math.uconn.edu Language: English - Date: 2010-07-30 13:32:03 Field theory Commutative algebra Homological algebra Module theory Algebraic number field Algebraic integer Ring of integers Torsion Integral element Abstract algebra Algebra Algebraic number theory
22	Armenian Journal of Mathematics Volume 5, Number 1, 2013, 58–68 Factor Rings and their decompositions in the Eisenstein integers Ring Z [ω] Manouchehr Misaghian Add to Reading List Source URL: ajm.asj-oa.am Language: English - Date: 2013-07-17 08:30:07 Number theory Modular arithmetic Algebraic number theory Commutative algebra Quadratic residue Quadratic reciprocity Root of unity Euclidean domain Coprime Abstract algebra Mathematics Algebra
23	Sage Reference Manual: Standard Commutative Rings Release 6.3 The Sage Development Team Add to Reading List Source URL: www.sagemath.org Language: English - Date: 2014-11-16 14:58:21 Ring theory Field theory Algebraic structures Algebraic number theory Commutative algebra Ring of integers Sage Ring Noetherian ring Abstract algebra Algebra Mathematics
24	The 35th International Mathematical Olympiad (July 13-14, 1994, Hong Kong) 1. Let m and n be positive integers. Let a1 , a2 , . . . , am be distinct elements of {1, 2, . . . , n} such that whenever ai + aj ≤ n for some Add to Reading List Source URL: media.hotnews.ro Language: English - Date: 2014-05-19 06:27:17 Ring theory Algebraic number theory Elementary number theory Integer Integer sequences Binomial coefficient Pythagorean triple Abstract algebra Mathematics Algebra
25	Algebraic K-theory of Number Fields Add to Reading List Source URL: www.algant.eu Language: English - Date: 2014-07-01 01:44:52 Mathematical analysis Field theory Meromorphic functions Analytic number theory Ring of integers Ring theory Riemann zeta function Algebraic number field Dedekind zeta function Abstract algebra Mathematics Algebraic number theory
26	Recollection Sheet • χ is a character on OK , the ring of integers of a quadratic imaginary field K of discriminant −D. •f = amq m is a weight 2 newform of level N , a rational Add to Reading List Source URL: eric.errthum.com Language: English - Date: 2006-08-24 07:29:46 Number theory Hecke character Symbol Weight Explicit formula Cyclotomic fields Dirichlet character Dirichlet L-function Abstract algebra Mathematics Algebra
27	UNITS GENERATING THE RING OF INTEGERS OF COMPLEX CUBIC FIELDS ROBERT F. TICHY AND VOLKER ZIEGLER Abstract. All purely cubic fields such that their maximal order is generated by its units are determined. Add to Reading List Source URL: finanz.math.tu-graz.ac.at Language: English - Date: 2010-09-29 02:35:12 Algebraic number field Field theory Symbol Algebraic integer Complex number Ring of integers Spectral theory of ordinary differential equations Riemann sphere Abstract algebra Algebraic number theory Algebra
28	Theorems of Sylvester and Schur T.N. Shorey An old theorem of Sylvester states that a product of k consecutive positive integers each exceeding k is divisible by a prime greater than k. We shall Add to Reading List Source URL: www.math.tifr.res.in Language: English - Date: 2007-07-25 06:46:24 Algebraic number theory Newton polygon Commutative algebra Localization Measure theory Valuation ring Radon–Nikodym theorem Abstract algebra Algebra Mathematics
29	52nd Mathematical Olympiad in Poland Problems of the first round, September – December[removed]Solve in integers the equation x2000 + [removed] = x1999 + [removed]The points D and E lie on the sides BC and AC of th Add to Reading List Source URL: www.mimuw.edu.pl Language: English - Date: 2000-11-27 07:44:18 Algebraic number theory Triangle geometry Ring theory Elementary number theory Integer Triangle Abstract algebra Mathematics Algebra
30	Computations of elliptic units for real quadratic fields Samit Dasgupta September 20, 2006 Contents 1 Definition of the units Add to Reading List Source URL: people.ucsc.edu Language: English - Date: 2008-09-13 15:52:31 Modular form Symbol P-adic number Valuation Ring of integers Vertex operator algebra Orbifold Abstract algebra Algebra Field theory