# principal ideal

## English[edit]

### Noun[edit]

**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*.

#### Synonyms[edit]

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