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Some Topological Properties of the Derivation Algebra D(K/k) for a Field Extension K/k
http://hdl.handle.net/10105/2308
http://hdl.handle.net/10105/23083d4e8e87-289c-4a21-a785-881193de2a9c
| 名前 / ファイル | ライセンス | アクション |
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NUE31_2_1-4.pdf (157.8 kB)
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| アイテムタイプ | 紀要論文 / Departmental Bulletin Paper(1) | |||||||
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| 公開日 | 2010-02-04 | |||||||
| タイトル | ||||||||
| タイトル | Some Topological Properties of the Derivation Algebra D(K/k) for a Field Extension K/k | |||||||
| 言語 | ||||||||
| 言語 | eng | |||||||
| 資源タイプ | ||||||||
| 資源タイプ | departmental bulletin paper | |||||||
| 著者 |
KIKUCHI, Teppei
× KIKUCHI, Teppei
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| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | Let K be a field extension of a field k, and D(K/k) be its derivation algebra. In the previous paper [1], we gave some topological considerations on D(K/k). And we showed, for example, that D(K/k) is dense in Homk(K,K) with respect to the finite topology if and only if the center Z(D)(K/k)) of D(K/k) coincides with k. On the other hand, we know already that D(K/k)＝D(K/ks) and Z(D(K/ks))⊃ks (where ks denotes the separable algebraic closure of k in K) and that if [K:k] is finite then D(K/k) is discrete. Consequently D(K/k) is discrete if [K:ks〕 is finite. In this paper first we show that the converses of these are false. That is, we show the existence of an example K/k such that Z(D(/k))≠ks and D(K/k) is discrete nevertheless [K:ks] is not finite. Next we shall prove that, under the assumption Z(D(K/k)) ＝k, D(K/k) is discrete if and only if [K:k] is finite. Finally we shall notice that, under a natural isomorphismΦ:Homk(K ？ K, K)CSH→Homk (K,K) such thatΦ(f)(x) ＝f(1 ？ x), Φ-1(D(K/k)) is the totality of the K-linear maps f:K ？ K→K which are continuous with respect to the Ik/k-adic topology of k ？ K and the discrete topology of K. Notation and terminology are the sarrle as [1], [2] and [3]. The finite topology of Homk(K, K) or D(K/k) defined in [1] will be called the finite k-topology in this paper. ？ means always ？ k. | |||||||
| 書誌情報 |
奈良教育大学紀要. 自然科学 巻 31, 号 2, p. 1-4, 発行日 1982-11-25 |
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| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 05472407 | |||||||
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| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AN00181070 | |||||||
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| 出版タイプ | VoR | |||||||
| 出版者 | ||||||||
| 出版者 | 奈良教育大学 | |||||||
