Bézout Domains with Nonzero Unit Radical
Yi Yang, Wolfgang Rump · Communications in Algebra · 2010
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 Krull , W. ( 1931 ). Allgemeine Bewertungstheorie . J. Reine Angew. Math. 167 : 160 – 196 . [Google Scholar]] for completely integrally closed Bézout domains D holds if u(D) ≠ 0.