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 1975, Chapter VII), (Raynaud 1970), and (Grothendieck 1967, Chapter 18).
In mathematics, a Henselianring (or Hensel ring) is a local ring in which Hensel's lemma holds. They were introduced by Azumaya (1951), who named them...
Nisnevich topology, the local rings are Henselian, and a finite cover of a Henselianring is given by a product of Henselianrings, showing exactness. If x...
converge to a point Hensel's lemma – Result in modular arithmetic Henselianring – local ring in which Hensel’s lemma holdsPages displaying wikidata descriptions...
real closed ring is a Henselianring (but in general local real closed domains are not valuation rings). The class of real closed rings is first-order...
hyperfields.Journal of Algebra, Volume 569, p. 416-441. Recall that in Henselianrings, any valuation extends uniquely to every algebraic extension of the...
Weierstrass ring, named by Nagata after Karl Weierstrass, is a commutative local ring that is Henselian, pseudo-geometric, and such that any quotient ring by a...
(Ditaxodon taeniatus), a snake endemic to southern Brazil Henselianring (also Hensel ring), a local ring in which Hensel's lemma holds Microtus henseli (also...
In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal. This means a DVR is an...
ISBN 978-3-540-63074-6 Gabber, Ofer (1992), "K-theory of Henselian local rings and Henselian pairs", Algebraic K-theory, commutative algebra, and algebraic...
local ring A in, say, B, need not be local. (If this is the case, the ring is called unibranch.) This is the case for example when A is Henselian and B...
projective geometry, the theory of separably closed local rings (aka “strictly Henselian local rings”) and the infinitary theory of torsion abelian groups;...
Alma mater Nagoya University Known for Azumaya algebra Krull–Azumaya theorem Henselianring Scientific career Fields Mathematics Institutions Indiana University...
algebraically closed field A field in which every variety has a rational point. Henselian field A field satisfying Hensel lemma w.r.t. some valuation. A generalization...
complete intersection (for example, regular) scheme over a henselian discrete valuation ring, then the constant sheaf shifted by dim X + 1 {\displaystyle...
Global Information