# principal ideal

## Contents

## EnglishEdit

### NounEdit

**principal ideal** (*plural* **principal ideals**)

- (algebra) An ideal
*I*in an algebraic object*R*(which could be a ring, algebra, semigroup or lattice) that is generated by a given single element*a*∈*R*; the smallest ideal that contains*a*.

#### SynonymsEdit

- (smallest ideal that contains a given element): two-sided principal ideal