nLab
principal ideal monoid

Contents

Context

Algebra

Monoid theory

Contents

Definition

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

Examples

A group is a principal ideal monoid GG whose only ideal is isomorphic to GG itself.

Last revised on May 21, 2021 at 18:24:25. See the history of this page for a list of all contributions to it.