nLab Bézout monoid

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Definition

A monoid (or semigroup) $M$ is a left Bézout monoid if all finitely generated left ideals of $M$ are left principal ideals in $M$ . Similarily, $M$ is a right Bézout monoid if all finitely generated right ideals of $M$ are right principal ideals. Finally, $M$ is a Bézout monoid if it is both a left Bézout monoid and a right Bézout monoid.

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