ガロア第一論文と乗数イデアル他関連資料スレ2

[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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358(3): 2023/03/13(月)21:11:52.56 ID:UeELXD7y(5/14) AAS
>>357
つづき

The claim
The key to the argument is the following

Claim. The set V of all elements a of D such that a2 <= 0 is a vector subspace of D of dimension n - 1. Moreover D = R 〇+ V as R-vector spaces, which implies that V generates D as an algebra.
Proof of Claim: Let m be the dimension of D as an R-vector space, and pick a in D with characteristic polynomial p(x). By the fundamental theorem of algebra, we can write

p(x)=(x-t_{1})\cdots (x-t_{r})(x-z_{1})(x-{\overline {z_{1}}})\cdots (x-z_{s})(x-{\overline {z_{s}}}),\qquad t_{i}\in \mathbf {R} ,\quad z_{j}\in \mathbf {C} \backslash \mathbf {R} .
省9

371: 2023/03/14(火)07:58:54.56 ID:5bTCTU61(2/7) AAS
>>369
>ウェッダーバーンの定理の証明なんて

手元に
雪江代数学3があるよ
P350 定理7.5.15 （ヴェーダーバーンの定理）
とある
証明は、2ページ弱
省4

501(2): 2023/03/18(土)16:08:11.56 ID:IyiE5s9T(3/12) AAS
>>498
改めて読み返したが、4元数体は体ではないので実数体の有限次拡大体ではない

586(1): 2023/03/19(日)11:31:17.56 ID:7NhejE26(8/14) AAS
>>567
>いわゆる「将棋の神様」から見れば、遥に遥に
>浅い所で遊んでいるに過ぎない。
>それは数学や物理でも同じことだろう。

同意
これからは、もっと数学にコンピュータAIが入ってくるだろう

過去、数値計算にコンピュータが導入され、円周率πの計算では、完全に人を凌駕した
省10

682: 2023/03/23(木)13:41:19.56 ID:gtBUMZjM(2/5) AAS
>>681
つづき

Oka's result has been generalized to domains spread over any Stein manifold: If such a domain D
is a pseudo-convex manifold, then D
is a Stein manifold. The Levi problem has also been affirmatively solved in a number of other cases, for example, for non-compact domains spread over the projective space CPn
or over a Kahler manifold on which there exists a strictly plurisubharmonic function (see ), and for domains in a Kahler manifold with positive holomorphic bisectional curvature [7]. At the same time, examples of pseudo-convex manifolds and domains are known that are not Stein manifolds and not even holomorphically convex. A necessary and sufficient condition for a complex space to be a Stein space is that it is strongly pseudo-convex (see Pseudo-convex and pseudo-concave). Also, a strongly pseudo-convex domain in any complex space is holomorphically convex and is a proper modification of a Stein space (see , [4] and also Modification; Proper morphism).
(引用終り)
省1

709(1): 2023/03/23(木)22:39:15.56 ID:aDRJxbk2(1) AAS
小松玄の弟子↓

Kengo Hirachi (平地健吾 Hirachi Kengo, born 30 November 1964) is a Japanese mathematician, specializing in CR geometry and mathematical analysis.

Hirachi received from Osaka University his B.S. in 1987, his M.S. in 1989, and his Dr.Sci., advised by Gen Komatsu, in 1994 with dissertation The second variation of the Bergman kernel for ellipsoids.[1] He was a research assistant from 1989 to 1996 and a lecturer from 1996 to 2000 at Osaka University. He was an associate professor from 2000 to 2010 and a full professor from 2010 to the present at the University of Tokyo. He was a visiting professor at the Mathematical Sciences Research Institute from October 1995 to September 1996, at the Erwin Schrödinger Institute for Mathematical Physics from March 2004 to April 2004, at Princeton University from October 2004 to July 2005, and at the Institute for Advanced Study from January 2009 to April 2009.

Awards and honors
Takebe Senior Prize (1999) of the Mathematical Society of Japan
Geometry Prize (2003) of the Mathematical Society of Japan
Stefan Bergman Prize (2006)
省2

813(2): 2023/03/28(火)22:02:48.56 ID:hsF37p1R(1) AAS
Michael Eastwood FAA is a mathematician at the University of Adelaide, known for his work in twistor theory, conformal differential geometry and invariant differential operators. In 1976 he received a PhD at Princeton University in several complex variables under Robert C. Gunning. He was a member of the twistor research group of Roger Penrose at the University of Oxford and he coauthored the monograph The Penrose Transform: Its Interaction with Representation Theory with Robert Baston. After moving to South Australia in 1985 he was the 1992 recipient of the Australian Mathematical Society Medal and made a Fellow of the Australian Academy of Science in 2005. In 2012 he was named to the inaugural (2013) class of fellows of the American Mathematical Society.

Rod Gover
Nationality New Zealander
Known for Invariant theory problems, operator classification problem
Scientific career
Fields Mathematics, differential geometry, theoretical physics
Thesis A Geometrical Construction of Conformally Invariant Differential Operators (1989)
省2

851(1): 2023/04/01(土)22:25:25.56 ID:EAl9sfTc(4/4) AAS
余因子行列ならよく見る

891: 2023/04/04(火)10:36:30.56 ID:gMUtsAok(1) AAS
>>889
>「行列初耳くん」もいるだろうから
>あえて私が「正方行列の逆行列」という
>表現をしたところ
　あえても炒めてもウソはウソじゃね？

>「正則行列を知らない！」と、
>揚げ足取りに騒ぐアホ
省13

976(2): 2023/04/08(土)20:56:23.56 ID:v/j/XuPX(1) AAS
時枝先生じゃなくても学部文系一般に鼻で笑われる阪大工学部。

お笑い種である。

989(1): 2023/04/09(日)11:44:23.56 ID:QDGuRhc1(1/3) AAS
>>987
数学で芸術的な完成度にこだわるのは
くだらないという立場？

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