Open AccessOn quadratic forms over semilocal rings
Author(s) -
Stefan Gille
Publication year - 2018
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/tran/7270
Subject(s) - mathematics , pure mathematics , ideal (ethics) , field (mathematics) , ring (chemistry) , perfect field , quadratic equation , quadratic form (statistics) , binary quadratic form , quadratic field , algebra over a field , combinatorics , quadratic function , geometry , law , chemistry , organic chemistry , political science
Using a recent result of Panin and Pimenov we show that several results, as for instance the linkage principle, in the algebraic theory of quadratic forms over fields also hold for quadratic forms over regular semilocal domains which contain a field of characteristic not 2. As an application we prove that the Arason and Elman presentation of the powers of the fundamental ideal of the Witt ring of a field extends to semilocal rings which contain an infinite field of characteristic not 2.