  It is proved that a ring $A$ is a right or left Noetherian, right
distributive centrally essential ring if and only if $A=A_1\times\cdots\times
A_n$, where each of the rings $A_i$ is either a commutative Dedekind domain or
a uniserial Artinian centrally essential (not necessarily commutative) ring.
  V.T.Markov is supported by the Russian Foundation for Basic Research, project
17-01-00895-A. A.A.Tuganbaev is supported by Russian Scientific Foundation,
project 16-11-10013.
