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• Integral domain
  In [[ring theory]], an '''integral domain''' is a [[commutativity|commutative]] [[ring (mathematics)|ring]] in which * A commutative ring is an integral domain if and only if the zero [[ideal]] is [[prime ideal|prime]].
  1,021 bytes (145 words) - 15:11, 30 October 2008
• Integral domain/Definition
  119 bytes (17 words) - 15:14, 30 October 2008
• Integral domain/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Integral domain]]. Needs checking by a human.
  675 bytes (89 words) - 17:28, 11 January 2010

Page text matches

• Dedekind domain/Related Articles
  {{r|integral domain}}
  356 bytes (46 words) - 13:02, 29 November 2008
• Integral domain
  In [[ring theory]], an '''integral domain''' is a [[commutativity|commutative]] [[ring (mathematics)|ring]] in which * A commutative ring is an integral domain if and only if the zero [[ideal]] is [[prime ideal|prime]].
  1,021 bytes (145 words) - 15:11, 30 October 2008
• Integral domain/Related Articles
  Auto-populated based on [[Special:WhatLinksHere/Integral domain]]. Needs checking by a human.
  675 bytes (89 words) - 17:28, 11 January 2010
• Divisor (ring theory)/Related Articles
  {{r|Integral domain}}
  516 bytes (65 words) - 16:01, 11 January 2010
• Localisation (ring theory)
  ...ns''' of ''R''. A ring can be embedded in a field if and only if it is an integral domain.
  2 KB (312 words) - 09:18, 21 October 2009
• Polynomial ring/Related Articles
  {{r|Integral domain}}
  770 bytes (96 words) - 19:39, 11 January 2010
• Commutativity/Related Articles
  {{r|Integral domain}}
  858 bytes (112 words) - 15:35, 11 January 2010
• Noetherian ring
  A '''Noetherian domain''' is a Noetherian ring which is also an [[integral domain]].
  2 KB (326 words) - 09:55, 23 December 2008
• Local ring
  ...lisation (ring theory)|localisation]] of a [[commutativity|commutative]] [[integral domain]] at a non-zero [[prime ideal]] is a local ring.
  844 bytes (130 words) - 12:09, 2 January 2009
• Rational number/Related Articles
  {{r|Integral domain}}
  1 KB (169 words) - 19:54, 11 January 2010
• Ring (mathematics)/Related Articles
  {{r|Integral domain}}
  1 KB (174 words) - 20:03, 11 January 2010
• Serge Lang/Related Articles
  {{r|Integral domain}}
  1 KB (187 words) - 20:18, 11 January 2010
• Algebra/Related Articles
  {{r|Integral domain}}
  2 KB (247 words) - 06:00, 7 November 2010
• Polynomial ring
  * If ''R'' is an [[integral domain]] then so is ''R''[''X''].
  4 KB (604 words) - 23:54, 20 February 2010
• Divisor (ring theory)
  ...re ''u'' is a unit, then ''a'' and ''b'' are associates. If ''R'' is an [[integral domain]], then the converse is true.
  2 KB (359 words) - 18:39, 2 December 2008
• Integer
  More formally, the integers are the only [[integral domain]] whose positive elements are [[well-ordered]], and this order is preserved ...ics)|ring]] with unity. Adding the last property says that '''Z''' is an [[integral domain]]. In fact, '''Z''' provides the motivation for defining such a structure.
  10 KB (1,566 words) - 08:34, 2 March 2024
• Algebraic number field
  The ring of integers is an [[integral domain]], but does not in general have the desirable factorisation properties of t
  7 KB (1,077 words) - 17:18, 10 January 2009
• Ring (mathematics)
  ** [[Integral domain]] (ID)
  10 KB (1,667 words) - 13:47, 5 June 2011
• Rational number
  ...ivalent in the above sense. (This construction can be carried out in any [[integral domain]]: see [[field of fractions]].)
  9 KB (1,446 words) - 08:52, 30 May 2009
• Fraction (mathematics)
  ...[field of fractions]], the smallest [[field (mathematics)|field]] of the [[integral domain]].
  21 KB (3,089 words) - 10:08, 28 February 2024