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
- Results about Bézout domains can be found here.
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.