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Abstract
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 [Citation4] for completely integrally closed Bézout domains D holds if u(D) ≠ 0.
ACKNOWLEDGMENT
We express our gratitude to the anonymous referee for her/his valuable comments and pointing out two gaps which led to an improvement of the presentation of this article.
The project sponsored by the Fund of Beijing Municipal Elitist Programme (Grant: 20071D1600600412), Beijing Municipal Natural Science Foundation (Grant: 1102027), SRF for ROCS, SEM, and Doctoral Fund of Ministry of Education of China (Grant: 20091102120045).
Notes
Communicated by J. Zhang.