nLab Bézout monoid

Contents

Context

Algebra

Monoid theory

Contents

Definition

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

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