  It is proved that a ring $R$ is a right uniserial, right Noetherian centrally
essential ring if and only if $R$ is a commutative discrete valuation domain or
a left and right Artinian, left and right uniserial ring. It is also proved
that there exist non-commutative uniserial Artinian centrally essential rings.
Victor Markov is supported by the Russian Foundation for Basic Research,
project 17-01-00895-A. Askar Tuganbaev is supported by Russian Scientific
Foundation, project 16-11-10013.
