ideal of elements with finite order
Theorem. The set of all elements of a ring, which have a finite order in the additive group of the ring, is a (two-sided) ideal of the ring.
Proof. Let be the set of the elements with finite order in the ring . Denote by the order of . Take arbitrary elements of the set .
If , then
Thus and so .
For any element of we have
Therefore, and . Similarly, .
Since satisfies the conditions for an ideal, the theorem has been proven.
|Title||ideal of elements with finite order|
|Date of creation||2013-03-22 17:52:30|
|Last modified on||2013-03-22 17:52:30|
|Last modified by||pahio (2872)|