Examples
- Any field is a Henselian local ring.
- Complete local rings, such as the ring of p-adic integers and rings of formal power series over a field, are Henselian.
- The rings of convergent power series over the real or complex numbers are Henselian.
- Rings of algebraic power series over a field are Henselian.
- A local ring that is integral over a Henselian ring is Henselian.
- The Henselization of a local ring is a Henselian local ring.
- Every quotient of a Henselian ring is Henselian.
- A ring A is Henselian if and only if the associated reduced ring Ared is Henselian (this is the quotient of A by the ideal of nilpotent elements).
- If A has only one prime ideal then it is Henselian since Ared is a field.
Read more about this topic: Henselian Ring
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