Principal ideal

This article defines a property of an ideal in a commutative unital ring |View other properties of ideals in commutative unital rings

This property of ideals in commutative unital rings depends only on the ideal, viewed abstractly as a module over the commutative unital ring. The corresponding module property that the ideal must satisfy is: cyclic module
View other such properties

Definition for commutative rings

Symbol-free definition

An ideal in a commutative unital ring is termed a principal ideal if it is the ideal generated by a single element of the ring.

Definition with symbols

An ideal $I$ in a ring $R$ is termed a principal ideal if there exists an $x$ in $R$ such that $I=Rx$.

Definition for noncommutative rings

Fill this in later