minus one times an element is the additive inverse in a ring
Let be a ring (with unity ) and let be an element of . Then
where is the additive inverse of and is the additive inverse of .
Note that for any in there exists a unique “” by the uniqueness of additive inverse in a ring. We check that equals the additive inverse of .
Hence is “an” additive inverse for , and by uniqueness , the additive inverse of . Analogously, we can prove that as well. ∎
|Title||minus one times an element is the additive inverse in a ring|
|Date of creation||2013-03-22 14:14:00|
|Last modified on||2013-03-22 14:14:00|
|Last modified by||alozano (2414)|