Right uniserial right Noetherian centrally essential rings are precisely commutative discrete valuation domains or two-sided Artinian two-sided uniserial rings, and non-commutative uniserial Artinian centrally essential rings exist.
Centrally essential rings which are no t necessarily unital or associative (Russian)
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Uniserial Noetherian Centrally Essential Rings
Right uniserial right Noetherian centrally essential rings are precisely commutative discrete valuation domains or two-sided Artinian two-sided uniserial rings, and non-commutative uniserial Artinian centrally essential rings exist.