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Some Remarks on High Order Derivations Ⅱ <Dedicated to Professor Yoshikazu Nakai on his 60th birthday>
http://hdl.handle.net/10105/2346
http://hdl.handle.net/10105/234674da9cc2-c546-405f-9388-b4980adba410
| 名前 / ファイル | ライセンス | アクション |
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NUE30_2_1-7.pdf (234.0 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 | 2010-02-05 | |||||||
| タイトル | ||||||||
| タイトル | Some Remarks on High Order Derivations Ⅱ <Dedicated to Professor Yoshikazu Nakai on his 60th birthday> | |||||||
| 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 A be a commutative ring with 1 and k be a subfield of A. In the previous papers [2] and [3], Y. Nakai and the author showed that the following three statements are equivalent, provided that A is a field. (1゜) D(A/k)＝Homk(A, A), where D(A/k) denotes the derivation algebra of A over k. (2゜) A is purely inseparable over k and [A : k]＜∞. (3゜) IA＝Ker(A？kA→A) is a nilpotent ideal of A？kA. Subsequently Y. Nakai proved that the statement (1゜) is equivalent in general (i.e. without assumption that A is a field) to the next statement ([4]). (2゜)′ A is a quasi-local ring with the maximal ideal m such that m is nilpotentand the residue field A/m is a purely inseparable and finite extension over k. Moreover his proof had an effect on making it clear that even (1゜) and (3゜) are equivalent in general, although it was not stated explicitly. However it seems to me that not a little part of his proof of (1゜)⇒(2゜)′ is based on our previous theorem. In this paper we shall try to give a simpler proof not making use of our previous theorem, as much as possible, except in the last stage. And we shall give a straightforward proof of the equivalence of (1゜) and (3゜) in general setting. The idea of the proofs of Prop. 5 and Lemma 6 is due to Nakai [4] and [5]. | |||||||
| 書誌情報 |
奈良教育大学紀要. 自然科学 巻 30, 号 2, p. 1-7, 発行日 1981-11-25 |
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| 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 | |||||||
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| 出版者 | 奈良教育大学 | |||||||
