Principal Ideal Domains
A principal ideal domain, or PID, is an integral domain in which every ideal is a principal ideal. A PID with only one non-zero maximal ideal is called a discrete valuation ring, or DVR, and every discrete valuation ring is a valuation ring. A valuation ring is a PID if and only if it is a DVR or a field. A value group is called discrete if and only if it is isomorphic to the additive group of the integers, and a valuation ring has a discrete valuation group if and only if it is a discrete valuation ring.
Read more about this topic: Valuation Ring
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