henselian
Word Rarity
Very rare
Frequency: Zipf frequency 0.00 in modern English
12
Scrabble Score
9
Letters
1
Syllables
7
Unique Chars
Meaning
adj
Which satisfies the criteria for (some formulation of) Hensel's lemma.
Example Sentences
- "1989, 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."
- "An analogous result holds for Henselian fields. Recall that a field K is said to be Henselian with respect to a valuation v if v has a unique extension (also denoted v) to every algebraic extension of K.[…]It follows that every algebraic extension of an^([sic]) Henselian field K is Henselian. […] Every valued field (K,v) has a minimal separable algebraic extension (K#95;v,v) which is Henselian. The valued field is unique up to a K-isomorphism and is called the Henselian closure of (K,v) [Ribenboim, p. 176]."
- "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."
Etymology
Word Breakdown
Phrases
Hensel ring
Frequently Paired Words
Henselization
Hensel ring