A discrete valuation ring (DVR) is a specific type of integral domain that has useful properties in algebraic geometry and number theory. Here are the key characteristics of a discrete valuation ring: 1. **Integral Domain**: A DVR is an integral domain, which means it is a commutative ring with no zero divisors and has a multiplicative identity (1 ≠ 0).
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A discrete valuation ring is a principal ideal domain with exactly one nonzero maximal ideal. Every nonzero element of its fraction field is a unit times a unique integer power of a uniformizer.