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Topic: Bezout domain characterization
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Michael Barr

Posts: 2
Registered: 6/8/12
Bezout domain characterization
Posted: Jun 8, 2012 2:32 PM
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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 non-unit of R.

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