User contributions for Vipul

14 May 2009

• 23:0523:05, 14 May 2009 diff hist +31‎ N Luroth's theorem ‎ moved Luroth's theorem to Lüroth's theorem current
• 23:0523:05, 14 May 2009 diff hist 0‎ m Lüroth's theorem ‎ moved Luroth's theorem to Lüroth's theorem
• 23:0423:04, 14 May 2009 diff hist +470‎ N Lüroth's theorem ‎ Created page with '==Statement== Let <math>K</math> be a field, and <math>K(t)</math> be the field of univariate rational functions, i.e., the field of rational functions in one variable over ...'
• 23:0023:00, 14 May 2009 diff hist +369‎ N Superreal field ‎ Created page with '{{field property}} ==Definition== A '''superreal field''' is a field isomorphic to the field of fractions of an integral domain of the form <math>C(X)/P</math>, where <math...' current
• 22:5722:57, 14 May 2009 diff hist −11‎ Archimedean and real-closed implies trivial automorphism group ‎ Redirected page to Archimedean and Euclidean implies trivial automorphism group current
• 22:5722:57, 14 May 2009 diff hist +74‎ N Archimedean and quadratically closed implies trivial automorphism group ‎ moved Archimedean and quadratically closed implies trivial automorphism group to Archimedean and Euclidean implies trivial automorphism group current
• 22:5722:57, 14 May 2009 diff hist 0‎ m Archimedean and Euclidean implies trivial automorphism group ‎ moved Archimedean and quadratically closed implies trivial automorphism group to Archimedean and Euclidean implies trivial automorphism group current
• 22:5722:57, 14 May 2009 diff hist −44‎ Archimedean and Euclidean implies trivial automorphism group ‎No edit summary
• 22:5622:56, 14 May 2009 diff hist +1,028‎ N Archimedean and Euclidean implies trivial automorphism group ‎ Created page with '{{field property implication| stronger = quadratically closed Archimedean field| weaker = field with trivial automorphism group}} ==Statement== Suppose <math>K</math> is a [[qu...'
• 22:3422:34, 14 May 2009 diff hist +85‎ N Archimedean and real-closed implies trivial automorphism group ‎ Redirected page to Archimedean and quadratically closed implies trivial automorphism group
• 22:3122:31, 14 May 2009 diff hist +650‎ N Number field ‎ Created page with '{{field property}} ==Definition== A '''number field''' is a field that is a finite extension of the field of rational numbers. ==Relation with other properties== ...' current
• 22:2922:29, 14 May 2009 diff hist +30‎ Template:Subfield-realizable ‎No edit summary current
• 22:2822:28, 14 May 2009 diff hist +1,009‎ Perfect field ‎No edit summary current
• 22:2422:24, 14 May 2009 diff hist +359‎ N Template:Subfield-realizable ‎ Created page with '{{quotation|''This field property is subfield-realizable: every field can be realized as a subfield of a field with this property.'...'
• 22:2322:23, 14 May 2009 diff hist +339‎ Algebraically closed field ‎No edit summary current
• 22:2122:21, 14 May 2009 diff hist +243‎ N Template:Odd-extension-closed ‎ Created page with '===Finite-extension-closedness=== {{quotation|''This field property is closed under taking finite extensions of odd degree. In other words, any finite extension of odd d...' current
• 22:2022:20, 14 May 2009 diff hist +2‎ Template:Finite-extension-closed ‎No edit summary current
• 22:2022:20, 14 May 2009 diff hist +376‎ N Template:Finite-extension-closed ‎ Created page with '===Finite-extension-closedness=== {{quotation|''This field property is closed under taking finite extensions. In other words, any finite extension of a field with this p...'
• 22:1822:18, 14 May 2009 diff hist +351‎ N Template:Subfield-closed ‎ Created page with '===Subfield-closedness=== {{quotation|''This field property is closed under taking subfields. In other words, any subfield of a field with this property also has this proper...' current
• 22:1622:16, 14 May 2009 diff hist +572‎ Formally real field ‎No edit summary current
• 22:0722:07, 14 May 2009 diff hist +32‎ N Template:Further ‎ Created page with '''Further information: {{{1}}}''' current
• 22:0722:07, 14 May 2009 diff hist +94‎ Perfect field ‎No edit summary
• 22:0622:06, 14 May 2009 diff hist +797‎ N Field of characteristic zero ‎ Created page with '{{field property}} ==Definition== A '''field of characteristic zero''' is defined in the following equivalent ways: # It is a field whose prime subfield is the [[defining ingr...' current
• 22:0422:04, 14 May 2009 diff hist +819‎ Formally real field ‎No edit summary
• 22:0122:01, 14 May 2009 diff hist +137‎ N Template:Proofofstrictimplicationat ‎ Created page with '''For proof of the implication, refer {{{1}}} and for proof of its strictness (i.e. the reverse implication being false) refer {{{2}}}''.' current
• 22:0122:01, 14 May 2009 diff hist +190‎ Archimedean field ‎ →‎Relation with other properties current
• 22:0022:00, 14 May 2009 diff hist +126‎ Archimedean field ‎No edit summary
• 21:5921:59, 14 May 2009 diff hist −297‎ Totally real field ‎ Redirected page to Archimedean field current
• 21:5721:57, 14 May 2009 diff hist +28‎ Field with trivial automorphism group ‎ →‎Relation with other properties current
• 21:5721:57, 14 May 2009 diff hist +328‎ N Totally real field ‎ Created page with '{{field property}} ==Definition== A '''totally real field''' is a field isomorphic to a subfield of the field of real numbers. ==Relation with other properties== ===W...'
• 21:5521:55, 14 May 2009 diff hist +905‎ N Archimedean field ‎ Created page with '{{field property}} ==Definition== An '''Archimedean field''' is a field with a total ordering <math>\le</math> on its elements satisfying the following: * <math>0 \le 1</m...'
• 21:4321:43, 14 May 2009 diff hist −56‎ Template:Top notice ‎No edit summary
• 21:4221:42, 14 May 2009 diff hist +402‎ N Template:Top notice ‎ Created page with '{{quotation|Welcome to '''{{fullsitetitle}}'''. This is a pre-alpha stage group theory wiki primarily managed by Vipul Naik, a Ph.D. student in Mathematics at the ...'
• 21:3921:39, 14 May 2009 diff hist −435‎ Main Page ‎ Replaced content with '{{top notice}}' current

10 May 2009

• 17:3117:31, 10 May 2009 diff hist +398‎ N Field with trivial Brauer group ‎ Created page with '{{field property}} ==Definition== A '''field with trivial Brauer group''' is a field whose defining ingredient:Brauer group is the trivial group. ==Relation with o...'
• 17:2817:28, 10 May 2009 diff hist +281‎ Algebraically closed field ‎No edit summary
• 17:2617:26, 10 May 2009 diff hist +287‎ Separably closed field ‎No edit summary current
• 17:2417:24, 10 May 2009 diff hist +454‎ N Separably closed field ‎ Created page with '{{field property}} ==Definition== A field is termed '''separably closed''' if it satisfies the following equivalent conditions: # Every irreducible polynomial over it ...'
• 17:2117:21, 10 May 2009 diff hist +616‎ N Quadratic extension ‎ Created page with '{{field extension property}} ==Definition== A field extension is termed a '''quadratic extension''' if it satisfies the following equivalent conditions: # It is the [[spli...' current
• 17:1817:18, 10 May 2009 diff hist +34‎ N Template:Proofat ‎ Created page with '''For full proof, refer: {{{1}}}''' current
• 17:1817:18, 10 May 2009 diff hist +479‎ N Field with trivial automorphism group ‎ Created page with '{{field property}} ==Definition== A '''field with trivial automorphism group''' is a field whose automorphism group i...'
• 17:1617:16, 10 May 2009 diff hist +861‎ N Real-closed field ‎ Created page with '==Definition== A '''real-closed field''' is a field satisfying the following equivalent conditions: # It is elementarily equivalent to the field of real numbers. # It is a ...' current
• 17:1217:12, 10 May 2009 diff hist +66‎ Euclidean field ‎ →‎Examples current
• 17:1117:11, 10 May 2009 diff hist +795‎ N Euclidean field ‎ Created page with '{{field property}} ==Definition== A '''Euclidean field''' is a field satisfying the following equivalent conditions: # The field is a [[defining ingredient::formally real ...'
• 17:0717:07, 10 May 2009 diff hist +540‎ N Quadratically closed field ‎ Created page with '{{field property}} ==Definition== A field is termed a '''quadratically closed field''' if every element in the field is a square. For every field, there is a unique smalle...' current
• 17:0117:01, 10 May 2009 diff hist +221‎ N Formally real field ‎ Created page with '{{field property}} ==Definition== A '''formally real field''' is a field in which <math>-1</math> is not a square. ==Relation with other properties== ===Stronger properti...'
• 17:0017:00, 10 May 2009 diff hist +305‎ N Pythagorean field ‎ Created page with '{{field property}} ==Definition== A '''Pythagorean field''' is a field in which a sum of squares is a square. ==Relation with other properties== ===Stronger properties=== * ...' current
• 16:5716:57, 10 May 2009 diff hist +66‎ Template:Field extension property ‎No edit summary current
• 16:5716:57, 10 May 2009 diff hist +330‎ N Template:Field extension property ‎ Created page with '{{quotation|''This article defines a field extension property: a property that can be evaluated to true/false for any field extension.''<br>[[:Category:Field extension pr...'
• 16:5516:55, 10 May 2009 diff hist +362‎ N Template:Field property ‎ Created page with '{{quotation|''This article defines a field property: a property that can be evaluated to true/false for any field.''<br>[[:Category:Field properties|View a complete list of f...' current