principal ideal ring
A commutative ring in which all ideals are principal (http://planetmath.org/PrincipalIdeal), i.e. (http://planetmath.org/Ie) generated by (http://planetmath.org/IdealGeneratedBy) a single ring element, is called a principal ideal ring. If is also an integral domain, it is a principal ideal domain
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Some well-known principal ideal rings are the ring of integers, its factor rings , and any polynomial ring over a field.