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Algebraic extension
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151	ALGORITHMS IN REAL ALGEBRAIC GEOMETRY: A SURVEY SAUGATA BASU Abstract. We survey both old and new developments in the theory of algorithms in real algebraic geometry – starting from effective quantifier elimination in Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2011-07-21 09:04:59 Real algebraic geometry Field theory Algebraic geometry Cylindrical algebraic decomposition Real closed field Algebraic extension Algebraic variety Tarski–Seidenberg theorem Field Abstract algebra Mathematics Algebra
152	ROOT NUMBERS AND RANKS IN POSITIVE CHARACTERISTIC B. CONRAD, K. CONRAD, AND H. HELFGOTT Abstract. For a global field K and an elliptic curve Eη over K(T ), Silverman’s specialization theorem implies rank(Eη (K(T ))) Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2005-10-02 23:07:54 Group theory Diophantine geometry Algebraic curves Abelian variety Birch and Swinnerton-Dyer conjecture Supersingular elliptic curve Finite field Separable extension Lenstra elliptic curve factorization Abstract algebra Elliptic curves Number theory
153	Artin’s Construction of an Algebraic Closure Patrick Morandi October 8, 2004 In this note we give a construction of an algebraic closure of an arbitrary …eld. This construction is due to Emil Artin. Zorn’s lemma is Add to Reading List Source URL: sierra.nmsu.edu Language: English - Date: 2004-10-08 10:16:24 Field theory Separable extension Field extension Algebraic closure Polynomial ring Irreducible polynomial Separable polynomial Algebraically closed field Splitting field Abstract algebra Algebra Polynomials
154	J. Eur. Math. Soc. 12, 529–553 c European Mathematical Society 2010 DOI[removed]JEMS/208 Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:22 Field theory Algebraic topology Betti number Topological graph theory Polynomial Algebraic variety Field extension Field Puiseux series Abstract algebra Mathematics Algebra
155	CLASSIFICATION OF PSEUDO-REDUCTIVE GROUPS BRIAN CONRAD AND GOPAL PRASAD Abstract. In an earlier work [CGP], a general theory for pseudo-reductive groups G over arbitrary fields k was developed, and a structure theorem wa Add to Reading List Source URL: math.stanford.edu Language: English - Date: 2013-12-17 09:51:09 Representation theory Lie groups Reductive group Root datum Field extension Separable extension Unipotent Gelfand pair Symmetric space Abstract algebra Algebra Algebraic groups
156	ARIZONA WINTER SCHOOL 2014 COURSE OUTLINE AND PROJECT DESCRIPTION: ASYMPTOTICS FOR NUMBER FIELDS AND CLASS GROUPS MELANIE MATCHETT WOOD ASSISTED BY: ROB HARRON Add to Reading List Source URL: swc.math.arizona.edu Language: English - Date: 2013-12-13 03:01:36 Algebraic number theory Manjul Bhargava Class field theory Kummer theory Ideal class group Galois group Algebraic number field Cubic field Field extension Abstract algebra Algebra Field theory
157	CLASS FIELD THEORY C. CIIEVALLEY NAGOYA UNIVEIWTY[removed] Add to Reading List Source URL: www.plouffe.fr Language: English - Date: 2014-05-28 20:51:53 Field theory Algebraic structures Ring theory Group theory Homomorphism Morphisms Valuation Field extension Ring Abstract algebra Algebra Mathematics
158	Algebraic Number Theory[removed]Field extensions (revision of algebraic prerequisites) Add to Reading List Source URL: www.plouffe.fr Language: English - Date: 2014-05-28 20:47:57 Separable extension Separable polynomial Field extension Field Finite field Integral element Galois theory Algebraic number field Irreducible polynomial Abstract algebra Algebra Field theory
159	1 1. FUNDAMENTALS E. L. Lady May 14, 1998 Add to Reading List Source URL: www.math.hawaii.edu Language: English - Date: 2001-04-07 05:40:29 Homological algebra Commutative algebra Algebraic number theory Torsion Divisible group Abelian group Finitely-generated module Dedekind domain Essential extension Abstract algebra Algebra Module theory
160	Fields and Galois Theory J.S. Milne Version 4.30, April 15, 2012 These notes give a concise exposition of the theory of fields, including Add to Reading List Source URL: www.jmilne.org Language: English - Date: 2012-04-15 16:51:59 Galois theory Algebraic number theory Group theory Algebraic structures Field Galois group Algebraic extension Abelian extension Évariste Galois Abstract algebra Algebra Field theory