Henselian

English Alternative forms en henselian Etymology From en Hensel ian surname; after German mathematician Kurt Hensel (1861–1941). Adjective - en algebra of a ring or field Which satisfies the criteria for (some formulation of) Hensel's lemma. 1989, Nicolas Bourbaki N. Bourbaki, Commutative Algebra: Chapters 1-7, [1985, N. Bourbaki, Éléments de Mathématique Algébre Commutative 1-4 et 5-7, Masson], Springer, page 256, A local ring satisfying conditions (H) and (C) is called Henselian. Every complete Hausdorff local ring is Henselian. If A is Henselian and B is a commutative A-algebra which is a local ring and a finitely generated A-module, then B is Henselian. en 2008 Michael D. Fried; Moshe Jarden Field Arithmetic 3rd https://books.google.com.au/books?id=FNkMaZrvpvsC&pg=PA203&dq=%22Henselian%22&hl=en&sa=X&ved=0ahUKEwixq_rt5cHcAhWJxrwKHRyABlIQ6AEIUzAI#v=onepage&q=%22Henselian%22&f=false 203 Springer An analogous result holds for Henselian fields. Recall that a field is said to be Henselian with respect to a valuation if has a unique extension (also denoted ) to every algebraic extension of .It follows that every algebraic extension of an Henselian field is Henselian. Every valued field has a minimal separable algebraic extension which is Henselian. The valued field is unique up to a -isomorphism and is called the Henselian closure of [Ribenboim, p. 176]. en 2017 Arno Fehm; Franziska Jahnke Recent progress on definability of Henselian valuations Fabrizio Broglia; Françoise Delon; Max Dickman; Danielle Gondard-Cozette; Victoria Ann Powers Ordered Algebraic Structures and Related Topics: International Conference w:American Mathematical Society https://books.google.com.au/books?id=xzo1DwAAQBAJ&pg=PA135&dq=%22Henselian%22&hl=en&sa=X&ved=0ahUKEwixq_rt5cHcAhWJxrwKHRyABlIQ6AEIQDAE#v=onepage&q=%22Henselian%22&f=false 136 Although the study of the definability of henselian valuations has a long history starting with J. Robinson, most of the results in this area were proven during the last few years. See also en Henselization en Hensel ring Further reading Henselian ring Hensel's lemma Anagrams en aeehilnns Hanelines en eponyms