[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ2 (1002ﾚｽ)
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360(2): 2023/03/13(月)21:13 ID:UeELXD7y(7/14) AAS
>>359
つづき

If n > 2, then D cannot be a division algebra. Assume that n > 2. Let u = e1e2en. It is easy to see that u2 = 1 (this only works if n > 2). If D were a division algebra, 0 = u2 ? 1 = (u ? 1)(u + 1) implies u = ±1, which in turn means: en = ?e1e2 and so e1, ..., en?1 generate D. This contradicts the minimality of W.

Remarks and related results
The fact that D is generated by e1, ..., en subject to the above relations means that D is the Clifford algebra of Rn. The last step shows that the only real Clifford algebras which are division algebras are Cｌ0, Cｌ1 and Cｌ2.
As a consequence, the only commutative division algebras are R and C. Also note that H is not a C-algebra. If it were, then the center of H has to contain C, but the center of H is R. Therefore, the only finite-dimensional division algebra over C is C itself.
This theorem is closely related to Hurwitz's theorem, which states that the only real normed division algebras are R, C, H, and the (non-associative) algebra O.
省3

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368: 2023/03/14(火)07:40 ID:bQV51cAg(1/8) AAS
>>367
１、検索結果を読んでも全く理解できず全コピペ

さすが大学１年の４月で落ちこぼれた真正●●

Q,　>>357-360を読んで肝心な部分をまとめて
　　　2048バイト以内（すなわち１コメント）で書け

１には絶対できないと予言する

勝った！（完全勝利宣言！！！）

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381(8): 2023/03/14(火)20:13 ID:bQV51cAg(3/8) AAS
>>377-379
東京●●大と大阪●●大
落ちこぼれ同士の共鳴

> 数学科以外で自分より上がいると、
> 落ちこぼれた自分がみじめで許せないんだ
　誰が上？貴様が？
　正則行列も知らず
省19

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