Thread: Algebra, Ring theory

Does anyone know how to show the following:

Suppose that R is a ring with identity, and suppose that 1R = 0R. Show that
R = { 0R }.

Thx guys.

Originally Posted by suedenation

Does anyone know how to show the following:

Suppose that R is a ring with identity, and suppose that 1R = 0R. Show that
R = { 0R }.

Thx guys.

I understand it as,

But because .
Thus,
.
Thus,
But, because .
Thus,
.
Q.E.D.