Matches in SemOpenAlex for { <https://semopenalex.org/work/W2017491518> ?p ?o ?g. }
Showing items 1 to 74 of
74
with 100 items per page.
- W2017491518 abstract "It is shown that quadratic extensions of a field not of characteristic two, which is linearly compact at a valuation, are determined by their groups of norms, provided the residue field has a unique quadratic extension and is perfect if of characteristic two. It is indicated that Henselian can replace linearly compact in some cases. Necessity of the condition on the residue field is shown. 1. In this brief paper we shall apply the techniques and results of the paper Quadratic extensions of linearly compact fields by Ron Brown and myself (referred to below as [BW]) to prove the following result: THEOREM 1. Let F be a field of characteristic char(F)$2. Let v be a (nonarchimedean) valuation on F with arbitrary value group rF and residue field kF; assume only that kF is perfect if char(kF)=2. Suppose that F is linearly compact at v and that kF has a unique quadratic extension. Then for K1 and K2 quadratic extensions of F, K1 K2 if and only if N1K1 = N2K2. (Here Ni denotes the norm map Ki-*F.) For definition and properties of linear compactness, see [BW] or [Bour]. All the hypotheses of Theorem 1 are satisfied by any classical local field of characteristic not two. Indeed Theorem 1 is a generalization of a special case of the local class field theorem which says that an abelian extension of a local field is determined by its group of norms. The conclusion of Theorem 1 is equivalent to the assertion that a binary quadratic form over F is determined up to equivalence by the elements of F which it represents. A straightforward application of the Global Squares Theorem extends this result to the global case, obtaining the well-known result that over any local or global field of characteristic not two, binary quadratic forms are equivalent if and only if they represent the same elements. Received by the editors July 9, 1971. AMS 1970 subject classifications. Primary 12B10, 12J10, 12B25; Secondary 10C05, 12A25, 12J20." @default.
- W2017491518 created "2016-06-24" @default.
- W2017491518 creator A5043915990 @default.
- W2017491518 date "1972-01-01" @default.
- W2017491518 modified "2023-09-24" @default.
- W2017491518 title "Determination of quadratic extensions of linearly compact fields by norm groups" @default.
- W2017491518 cites W2015227148 @default.
- W2017491518 cites W2065071234 @default.
- W2017491518 cites W2101104875 @default.
- W2017491518 doi "https://doi.org/10.1090/s0002-9939-1972-0294308-3" @default.
- W2017491518 hasPublicationYear "1972" @default.
- W2017491518 type Work @default.
- W2017491518 sameAs 2017491518 @default.
- W2017491518 citedByCount "0" @default.
- W2017491518 crossrefType "journal-article" @default.
- W2017491518 hasAuthorship W2017491518A5043915990 @default.
- W2017491518 hasBestOaLocation W20174915181 @default.
- W2017491518 hasConcept C118615104 @default.
- W2017491518 hasConcept C129844170 @default.
- W2017491518 hasConcept C134306372 @default.
- W2017491518 hasConcept C136170076 @default.
- W2017491518 hasConcept C166437778 @default.
- W2017491518 hasConcept C17744445 @default.
- W2017491518 hasConcept C191795146 @default.
- W2017491518 hasConcept C199539241 @default.
- W2017491518 hasConcept C202444582 @default.
- W2017491518 hasConcept C2524010 @default.
- W2017491518 hasConcept C2781025942 @default.
- W2017491518 hasConcept C33923547 @default.
- W2017491518 hasConcept C80695182 @default.
- W2017491518 hasConcept C95136341 @default.
- W2017491518 hasConcept C9652623 @default.
- W2017491518 hasConceptScore W2017491518C118615104 @default.
- W2017491518 hasConceptScore W2017491518C129844170 @default.
- W2017491518 hasConceptScore W2017491518C134306372 @default.
- W2017491518 hasConceptScore W2017491518C136170076 @default.
- W2017491518 hasConceptScore W2017491518C166437778 @default.
- W2017491518 hasConceptScore W2017491518C17744445 @default.
- W2017491518 hasConceptScore W2017491518C191795146 @default.
- W2017491518 hasConceptScore W2017491518C199539241 @default.
- W2017491518 hasConceptScore W2017491518C202444582 @default.
- W2017491518 hasConceptScore W2017491518C2524010 @default.
- W2017491518 hasConceptScore W2017491518C2781025942 @default.
- W2017491518 hasConceptScore W2017491518C33923547 @default.
- W2017491518 hasConceptScore W2017491518C80695182 @default.
- W2017491518 hasConceptScore W2017491518C95136341 @default.
- W2017491518 hasConceptScore W2017491518C9652623 @default.
- W2017491518 hasLocation W20174915181 @default.
- W2017491518 hasOpenAccess W2017491518 @default.
- W2017491518 hasPrimaryLocation W20174915181 @default.
- W2017491518 hasRelatedWork W141438329 @default.
- W2017491518 hasRelatedWork W1854612299 @default.
- W2017491518 hasRelatedWork W1872266260 @default.
- W2017491518 hasRelatedWork W1988007937 @default.
- W2017491518 hasRelatedWork W1991129564 @default.
- W2017491518 hasRelatedWork W2010748967 @default.
- W2017491518 hasRelatedWork W2047406140 @default.
- W2017491518 hasRelatedWork W2049392516 @default.
- W2017491518 hasRelatedWork W2065071234 @default.
- W2017491518 hasRelatedWork W2067718134 @default.
- W2017491518 hasRelatedWork W2079564395 @default.
- W2017491518 hasRelatedWork W2079627142 @default.
- W2017491518 hasRelatedWork W2086399879 @default.
- W2017491518 hasRelatedWork W2262452343 @default.
- W2017491518 hasRelatedWork W2372319987 @default.
- W2017491518 hasRelatedWork W242137141 @default.
- W2017491518 hasRelatedWork W2503472695 @default.
- W2017491518 hasRelatedWork W2607301120 @default.
- W2017491518 hasRelatedWork W3023018820 @default.
- W2017491518 hasRelatedWork W9766112 @default.
- W2017491518 isParatext "false" @default.
- W2017491518 isRetracted "false" @default.
- W2017491518 magId "2017491518" @default.
- W2017491518 workType "article" @default.