現代数学の系譜工学物理雑談古典ガロア理論も読む78

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む78 (1002ﾚｽ)
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357: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/11/01(金) 21:28:22.52 ID:rcKeDs9u

>>345
どうも。スレ主です。
フォローありがとう

追加参考
https://ja.wikipedia.org/wiki/%E4%BD%93_(%E6%95%B0%E5%AD%A6)
体 (数学)
(抜粋)
この代数的構造はリヒャルト・デーデキントとレオポルト・クロネッカーがそれぞれ独立に（そして極めて異なる方法で）導入したが、体という呼称は実数または複素数からなる四則演算に関して閉じている部分集合を表すものとしてドイツ語で体を意味する Korper を用いたのが由来である（それがゆえに、任意の体を表すのにしばしば K をプレースホルダとして用いる）。

https://zh.wikipedia.org/wiki/%E5%9F%9F_(%E6%95%B8%E5%AD%B8)
中国
域 数学

https://en.wikipedia.org/wiki/Field_(mathematics)
Field (mathematics)
(抜粋)
History
Historically, three algebraic disciplines led to the concept of a field: the question of solving polynomial equations, algebraic number theory, and algebraic geometry.[15] A first step towards the notion of a field was made in 1770 by Joseph-Louis Lagrange,

Vandermonde, also in 1770, and to a fuller extent, Carl Friedrich Gauss, in his Disquisitiones Arithmeticae (1801),

These gaps were filled by Niels Henrik Abel in 1824.[18] Evariste Galois, in 1832, devised necessary and sufficient criteria for a polynomial equation to be algebraically solvable, thus establishing in effect what is known as Galois theory today.
Both Abel and Galois worked with what is today called an algebraic number field, but conceived neither an explicit notion of a field, nor of a group.

In 1871 Richard Dedekind introduced, for a set of real or complex numbers that is closed under the four arithmetic operations, the German word Korper, which means "body" or "corpus" (to suggest an organically closed entity). The English term "field" was introduced by Moore (1893).[19]

つづく

http://rio2016.5ch.net/test/read.cgi/math/1571400076/357

358: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/11/01(金) 21:31:23.15 ID:rcKeDs9u

>>357

つづき

By a field we will mean every infinite system of real or complex numbers so closed in itself and perfect that addition, subtraction, multiplication, and division of any two of these numbers again yields a number of the system.
??Richard Dedekind, 1871[20]

In 1881 Leopold Kronecker defined what he called a domain of rationality, which is a field of rational fractions in modern terms.
Kronecker's notion did not cover the field of all algebraic numbers (which is a field in Dedekind's sense),
but on the other hand was more abstract than Dedekind's in that it made no specific assumption on the nature of the elements of a field. Kronecker interpreted a field such as Q(π) abstractly as the rational function field Q(X).
Prior to this, examples of transcendental numbers were known since Joseph Liouville's work in 1844, until Charles Hermite (1873) and Ferdinand von Lindemann (1882) proved the transcendence of e and π, respectively.[21]

The first clear definition of an abstract field is due to Weber (1893).[22]
In particular, Heinrich Martin Weber's notion included the field Fp. Giuseppe Veronese (1891) studied the field of formal power series, which led Hensel (1904) to introduce the field of p-adic numbers.
Steinitz (1910) synthesized the knowledge of abstract field theory accumulated so far. He axiomatically studied the properties of fields and defined many important field-theoretic concepts.
The majority of the theorems mentioned in the sections Galois theory, Constructing fields and Elementary notions can be found in Steinitz's work.
Artin & Schreier (1927) linked the notion of orderings in a field, and thus the area of analysis, to purely algebraic properties.[23]
Emil Artin redeveloped Galois theory from 1928 through 1942, eliminating the dependency on the primitive element theorem.
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1571400076/358

366: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/11/02(土) 07:01:37.05 ID:ZLEqKHqI

>>357
> The English term "field" was introduced by Moore (1893).[19]

E. H. Moore（1862 ? 1932)さん
("Robert Lee Moore (no relation) Topologist (1882 ? 1974) " は、別人ですね)
（参考）
https://en.wikipedia.org/wiki/E._H._Moore
(抜粋)
Eliakim Hastings Moore (/??la??k?m/; January 26, 1862 ? December 30, 1932), usually cited as E. H. Moore or E. Hastings Moore, was an American mathematician.

Accomplishments

In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. Independently,[2] during a course taught by G. B. Halsted, the twenty-year-old Robert Lee Moore (no relation) also proved this, but in a more elegant fashion than E. H. Moore used.

At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore (no relation), and Oswald Veblen. Birkhoff and Veblen went on to lead departments at Harvard and Princeton, respectively.
Dickson became the first great American algebraist and number theorist. Robert Moore founded American topology. According to the Mathematics Genealogy Project, as of December 2012, E. H. Moore had over 18,900 known "descendants."

https://en.wikipedia.org/wiki/Robert_Lee_Moore
(抜粋)
Robert Lee Moore (November 14, 1882 ? October 4, 1974) was an American mathematician who taught for many years at the University of Texas.
He is known for his work in general topology, for the Moore method of teaching university mathematics, and for his poor treatment of African-American mathematics students.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1571400076/366

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