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.

Last revised on May 21, 2021 at 18:26:26. See the history of this page for a list of all contributions to it.