additive inverse of an inverse element
In any ring R, the additive inverse of an element a∈R must exist, is unique and is denoted by -a. Since -a is also in the ring R it also has an additive inverse in R, which is -(-a). Put -(-a)=c∈R. Then by definition of the additive inverse, -a+c=0 and -a+a=0. Since additive inverses are unique, it must be that c=a.
| Title | additive inverse of an inverse element |
|---|---|
| Canonical name | AdditiveInverseOfAnInverseElement |
| Date of creation | 2013-03-22 15:45:16 |
| Last modified on | 2013-03-22 15:45:16 |
| Owner | Mathprof (13753) |
| Last modified by | Mathprof (13753) |
| Numerical id | 8 |
| Author | Mathprof (13753) |
| Entry type | Result |
| Classification | msc 16B70 |
| Related topic | InverseOfInverseInAGroup |