group of units
Proof. If and are two units, then there are the elements and of such that and . Then we get that , similarly . Thus also is a unit, which means that is closed under multiplication. Because and along with also its inverse belongs to , the set is a group.
Corollary. In a commutative ring, a ring product is a unit iff all are units.
When , then .
When , the ring of Gaussian integers, then .
When , then (http://planetmath.org/UnitsOfQuadraticFields) .
When where is a field, then .
|Title||group of units|
|Date of creation||2013-03-22 14:41:32|
|Last modified on||2013-03-22 14:41:32|
|Last modified by||pahio (2872)|
|Defines||group of units of ring|
|Defines||multiplicative group of field|