redundancy of two-sidedness in definition of group
The group may also be defined without the two-sidednesses:
2) any element of has a right inverse .
We have to show that the right identity is also a left identity and that any right inverse is also a left inverse.
Let the above assumptions on be true. If is the right inverse of an arbitrary element of , the calculation
shows that it is also the left inverse of . Using this result, we then can write
whence is a left identity element, too.
|Title||redundancy of two-sidedness in definition of group|
|Date of creation||2015-01-20 17:28:03|
|Last modified on||2015-01-20 17:28:03|
|Last modified by||pahio (2872)|