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Algebra Comput."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p> A ring R is said to be centrally essential if for every its nonzero element a, there exist nonzero central elements x and y with [Formula: see text]. A ring R is said to be completely centrally essential if all its factor rings are centrally essential rings. It is proved that completely centrally essential semiprimary rings are Lie nilpotent; noetherian completely centrally essential rings are strongly Lie nilpotent (in particular, every such ring is a [Formula: see text]-ring). Every completely centrally essential ring has the classical ring of fractions which is a completely centrally essential ring. 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