  In recent years, centrally essential rings have been intensively studied in
ring theory. In particular, they find applications in homological algebra,
group rings, and the structural theory of rings. The class of essentially
central rings strongly extends the class of commutative rings. For such rings,
a number of recent papers contain positive answers to some important questions
from ring theory that previously had positive answers for commutative rings and
negative answers in the general case. This work is devoted to a similar topic.
A familiar description of right Noetherian, right distributive centrally
essential rings is generalized on a larger class of rings. Let $A$ be a ring
with prime radical $P(A)$. It is proved that $A$ is a right distributive, right
invariant centrally essential ring and $P(A)$ is a finitely generated right
ideal such that the factor-ring $A/P(A)$ does non contain an infinite direct
sum of non-zero ideals if and only if $A=A_1\times\cdots\times A_n$, where
every ring $A_k$ is either a commutative Pr\"ufer domain or an Artinian
uniserial ring.
