Throughout R is a ring with right singular ideal
Z
(
R
)
Z(R)
. A right ideal K of R is rationally closed if
x
−
1
K
=
{
y
∈
R
:
x
y
∈
K
}
{x^{ - 1}}K = \{ y \in R:xy \in K\}
is not a dense right ideal for all
x
∈
R
−
K
x \in R - K
. A ring R is a Cl-ring if R is (Goldie) right finite dimensional,
R
/
Z
(
R
)
R/Z(R)
is semiprime,
Z
(
R
)
Z(R)
is rationally closed, and
Z
(
R
)
Z(R)
contains no closed uniform right ideals. These rings include the quasi-Frobenius rings as well as the semiprime Goldie rings. The commutative Cl-rings have Cl-classical quotient rings. The injective ones are congenerator rings. In what follows, R is a Cl-ring. A dense right ideal of R contains a right nonzero divisor. If R satisfies the minimum condition on rationally closed right ideals then R has a classical Artinian quotient ring. The complete right quotient ring Q (also called the Johnson-Utumi maximal quotient ring) of R is a Cl-ring. If R has the additional property that bR is dense whenever b is a right nonzero divisor, then Q is classical. If Q is injective, then Q is classical.