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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Brauer's theorem on forms ： ウィキペディア英語版 Brauer's theorem on forms :''There also is Brauer's theorem on induced characters.'' In mathematics, Brauer's theorem, named for Richard Brauer, is a result on the representability of 0 by forms over certain fields in sufficiently many variables.〔R. Brauer, ''A note on systems of homogeneous algebraic equations'', Bulletin of the American Mathematical Society, 51, pages 749-755 (1945)〕 ==Statement of Brauer's theorem== Let ''K'' be a field such that for every integer ''r'' > 0 there exists an integer ψ(''r'') such that for ''n'' ≥ ψ(r) every equation :$($ *)\qquad a_1x_1^r+\cdots+a_nx_n^r=0,\quad a_i\in K,\quad i=1,\ldots,n has a non-trivial (i.e. not all ''x''''i'' are equal to 0) solution in ''K''. Then, given homogeneous polynomials ''f''1,...,''f''''k'' of degrees ''r''1,...,''r''''k'' respectively with coefficients in ''K'', for every set of positive integers ''r''1,...,''r''''k'' and every non-negative integer ''l'', there exists a number ω(''r''1,...,''r''''k'',''l'') such that for ''n'' ≥ ω(''r''1,...,''r''''k'',''l'') there exists an ''l''-dimensional affine subspace ''M'' of ''Kn'' (regarded as a vector space over ''K'') satisfying :$f\_1(x\_1,\backslash ldots,x\_n)=\backslash cdots=f\_k(x\_1,\backslash ldots,x\_n)=0,\backslash quad\backslash forall(x\_1,\backslash ldots,x\_n)\backslash in\; M.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Brauer's theorem on forms」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.