Difference between revisions of "Ring (mathematics)"
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| − | A '''ring''' in [[mathematics]] is a set ''R'' equipped with two [[binary]] [[ | + | A '''ring''' in [[mathematics]] is a set ''R'' equipped with two [[binary]] [[operation]]s, usually called addition and multiplication, satisfying that |
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'''2.''' ''R'' with multiplication is a [[semigroup]]; | '''2.''' ''R'' with multiplication is a [[semigroup]]; | ||
| − | '''3.''' multiplication [[ | + | '''3.''' multiplication [[distribute]]s over addition. |
Revision as of 01:48, February 26, 2008
A ring in mathematics is a set R equipped with two binary operations, usually called addition and multiplication, satisfying that
1. R with addition is a commutative group;
2. R with multiplication is a semigroup;
3. multiplication distributes over addition.
Remarks
A ring with unit is a ring for which multiplication has a neutral element.
A division ring is a ring such that R with multiplication is a (not necessarily commutative) group.