  Two elements $a,b$ in a ring $R$ form a right coprime pair, written $\langle
a,b\rangle$, if $aR+bR=R$. Right coprime pairs have shown to be quite useful in
the study of left cotorsion or exchange rings. In this paper, we define the
class of strongly right exchange rings in terms of descending chains of them.
We show that they are semiregular and that this class of rings contains left
injective, left pure-injective, left cotorsion, local and left continuous
rings. This allows us to give a unified study of all these classes of rings in
terms of the behaviour of descending chains of right coprime pairs.
