Definition:Bézout Domain

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Definition

Definition 1

A Bézout domain is an integral domain in which the sum of two principal ideals is again principal.


Definition 2

A Bézout domain is an integral domain in which every finitely generated ideal is principal.


Also see


Source of Name

This entry was named for Étienne Bézout.


Historical Note

The definition of an integral domain, and even that of a ring, was not formulated until over a century after the death of Étienne Bézout.

However, a Bézout domain bears his name because in such an algebraic structure, each pair of elements satisfies an algebraic formulation of Bézout's Identity.