Difference between revisions of "Ring (mathematics)"
Jump to navigation
Jump to search
| Line 15: | Line 15: | ||
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]]. | ||
| − | [[Category: | + | [[Category:Algebra]] |
Revision as of 16:46, April 1, 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.