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- 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
- 119 bytes (17 words) - 15:14, 30 October 2008
- Auto-populated based on [[Special:WhatLinksHere/Integral domain]]. Needs checking by a human.675 bytes (89 words) - 17:28, 11 January 2010
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- {{r|integral domain}}356 bytes (46 words) - 13:02, 29 November 2008
- 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
- Auto-populated based on [[Special:WhatLinksHere/Integral domain]]. Needs checking by a human.675 bytes (89 words) - 17:28, 11 January 2010
- {{r|Integral domain}}516 bytes (65 words) - 16:01, 11 January 2010
- ...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
- {{r|Integral domain}}770 bytes (96 words) - 19:39, 11 January 2010
- {{r|Integral domain}}858 bytes (112 words) - 15:35, 11 January 2010
- A '''Noetherian domain''' is a Noetherian ring which is also an [[integral domain]].2 KB (326 words) - 09:55, 23 December 2008
- ...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
- {{r|Integral domain}}1 KB (169 words) - 19:54, 11 January 2010
- {{r|Integral domain}}1 KB (174 words) - 20:03, 11 January 2010
- {{r|Integral domain}}1 KB (187 words) - 20:18, 11 January 2010
- {{r|Integral domain}}2 KB (247 words) - 06:00, 7 November 2010
- * If ''R'' is an [[integral domain]] then so is ''R''[''X''].4 KB (604 words) - 23:54, 20 February 2010
- ...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
- 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
- The ring of integers is an [[integral domain]], but does not in general have the desirable factorisation properties of t7 KB (1,077 words) - 17:18, 10 January 2009
- ** [[Integral domain]] (ID)10 KB (1,667 words) - 13:47, 5 June 2011
- ...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
- ...[field of fractions]], the smallest [[field (mathematics)|field]] of the [[integral domain]].21 KB (3,089 words) - 10:08, 28 February 2024