Clifland

2021-01-31

Suppose that R is a ring and that ${a}^{2}=a$ for all $a\in RZ$ . Show that R
is commutative.

Bertha Stark

Skilled2021-02-01Added 96 answers

For any

Now, let

Adding ba on both sides of above equation, we get,

From equation 1, we can observe that same terms on both sides of equation get cancelled out.

So, applying same observation on equation 2, we get,

Hence, Ring R is commutative.

Kamal EL-saady

Beginner2022-05-26Added 1 answers