Difference between revisions of "Ring (mathematics)"
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A '''division ring''' is a ring such that ''R'' with multiplication is a (not necessarily [[commutative]]) [[group]]. | A '''division ring''' is a ring such that ''R'' with multiplication is a (not necessarily [[commutative]]) [[group]]. | ||
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| + | [[Category:Mathematics]] | ||
Revision as of 10:36, March 11, 2007
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.