TOPICS

Principal Ideal


An ideal I of a ring R is called principal if there is an element a of R such that

 I=aR={ar:r in R}.

In other words, the ideal is generated by the element a. For example, the ideals nZ of the ring of integers Z are all principal, and in fact all ideals of Z are principal.


See also

Ideal, Principal Ring, Ring

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Principal Ideal." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrincipalIdeal.html

Subject classifications