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Bezout domain characterization
Posted:
Jun 8, 2012 2:32 PM


In the course of studying something else, I have proved the following. It seems much too elementary and basic not to be known. Can someone give a reference?
Theorem. Let R be a UFD. Then R is a Bezout domain iff every proper rational extension of R (that is a ring between R and its field of fractions) contains the inverse of some nonunit of R.



