Distributive lattices

I have a question which is in my ring theory lesson. it's under the topic of distributive lattice and I don't know how to prove it.

Que: If A is a strongly regular ring, then the principle right ideals of A form a boolean algebra wich is isomorphic to the boolean algebra of A.

I want some ideas which clear my mind.

When $$A$$ is strongly regular, idempotents are all central, and each principle ideal is generated by a unique idempotent.
One can easily check that the lattice of principal right ideals (they are all ideals, actually) reflects exactly the the partial order $$a\leq b\iff ab=a$$ on the idempotents of $$A$$ through the map $$e\mapsto eA$$.