additive inverse of an inverse element

In any ring R, the additive inverse of an element aR 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)=cR. 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