Page "Principal ideal domain" Paragraph 0

In abstract algebra, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i. e., can be generated by a single element.

More generally, a principal ideal ring is a nonzero commutative ring whose ideals are principal, although some authors ( e. g., Bourbaki ) refer to PIDs as principal rings.

The distinction is that a principal ideal ring may have zero divisors whereas a principal ideal domain cannot.