In mathematics, a Henselian ring (or Hensel ring) is a local ring in which Hensel's lemma holds. They were introduced by Azumaya (1951), who named them after Kurt Hensel. Azumaya originally allowed Henselian rings to be non-commutative, but most authors now restrict them to be commutative.
Some standard references for Hensel rings are (Nagata 1962, Chapter VII), (Raynaud 1970), and (Grothendieck 1967, Chapter 18).
Read more about Henselian Ring: Definitions, Henselian Rings in Algebraic Geometry, Henselization, Examples
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