hamidreza dorbidi

In this paper we study rings which x^2 = a^2 implies x = +-a. We call a ring with this property a Q-ring. For example integral domains and Boolean rings are Q-rings. But the ring of real quaternions is not a Q-ring. Also every reduced commutative ring of characteristic two is a Q-ring. Every Q-ring is reduced. We give some other necessary conditions which satisfied by Q-rings. We prove that if ab = 0 in a Q-ring then 2a = 0 or 2b = 0. We Show that if D is an odd dimensional division ring over its center, then D is a Q-ring.