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

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Cite this as:

Weisstein, Eric W. "Principal Ideal." From MathWorld--A Wolfram Web Resource.

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