Let R be a ring with involution.
There exists a unique maximal nilpotent ∗-ideal N of R such that R∕N with the
induced involution satisfies the property that any regular element ot S, the subring
generated by the symmetric elements of R∕N is regular in R∕N. When N = 0 we say
that R satisfies the regularity condition. Assuming this condition, (Q(R)) = R if and
only if Q(S) =S. The existence of Q(S) implies the existence of Q(R), and the
converse is shown in some special cases. If either S is commutative or R is a
semi-prime Goldie ring, then the relation between Q(R) and Q(S) is explicitly
described.
