A Bézout domain is an integral domain in which every finitely generated ideal is principal. Equivalently, every pair has a greatest common divisor satisfying a Bézout identity . A Noetherian Bézout domain is a principal ideal domain because all its ideals are finitely generated.
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A Bézout domain is a specific type of integral domain in abstract algebra that possesses a particular property related to the linear combinations of its elements.