Bézout domains with nonzero unit radical

For an integral domain D, we define the unit radical u (D) which gives a ring theoretic characterization for a strong unit of the group of divisibility, then we show that the radical of a μ-normal-valued unital l-group is generated by bounded elements. Consequently, we get an explicit description of the minimal completely integrally closed overorder for a Bézout domain D with u D ≠ 0. Especially, we verify that Krull's conjecture [4] for completely integrally closed Bézout domains D holds if u D ≠ 0.