Question

Let r be a ring such that x²=x for all x in r

Answer 1

In a ring where x^2 = x for all x, the elements of the ring can only be 0 and 1.

Step-by-step explanation:

In a ring r where x^2 = x for all x in r, we can solve this equation by recognizing that the left side of the equation is a perfect square.

So, we have x^2 - x = 0, which simplifies to x(x - 1) = 0. This equation has two solutions, either x = 0 or x = 1.

Therefore, the elements of the ring r can only be 0 and 1.