nLab
principal ideal of a monoid

Contents

Context

Algebra

Monoid theory

Contents

Definition

Given a monoid (or semigroup) MM and an element aMa \in M, a left principal ideal in MM is a subset MaM a of MM such that for all mMm \in M, maMam a \in M a. Similarly, a right principal ideal in MM is a subset aMa M of MM such that for all mMm \in M, amaMa m \in a M. Finally, a two-sided principal ideal, or simply principal ideal, in MM is a subset a\langle a \rangle that is both a left ideal and a right ideal.

Last revised on May 21, 2021 at 18:23:57. See the history of this page for a list of all contributions to it.