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Emmy Noether was a German mathematician. This article lists the publications upon which her reputation is built (in part). ==First epoch (1908–1919)== | ''Journal für die reine und angewandte Mathematik'', 134, 23–90 + 2 tables || Algebraic invariants. Main description of her dissertation, including 331 explicitly calculated ternary invariants. |- | 3 || 1910 || (Zur Invariantentheorie der Formen von ''n'' Variabeln ) | ''Jahresbericht der Deutschen Mathematiker-Vereinigung'', 19, 101–104 || Algebraic invariants. Short communication describing the following paper. |- | 4 || 1911 || (Zur Invariantentheorie der Formen von ''n'' Variabeln ) | ''Journal für die reine und angewandte Mathematik'', 139, 118–154 || Algebraic invariants. Extension of the formal algebraic-invariant methods to forms of an arbitrary number ''n'' of variables. Noether applied these results in her publications #8 and #16. |- | 5 || 1913 || (Rationale Funktionenkörper ) | ''Jahresbericht der Deutschen Mathematiker-Vereinigung'', 22, 316–319 || Field theory. See the following paper. |- | 6 || 1915 || (Körper und Systeme rationaler Funktionen ) | ''Mathematische Annalen'', 76, 161–191 || Field theory. In this and the preceding paper, Noether investigates fields and systems of rational functions of ''n'' variables, and demonstrates that they have a rational basis. In this work, she combined then-recent work of Ernst Steinitz on fields, with the methods for proving finiteness developed by David Hilbert. The methods she developed in this paper appeared again in her publication #11 on the inverse Galois problem. |- |- | 7 || 1915 || (Der Endlichkeitssatz der Invarianten endlicher Gruppen ) | ''Mathematische Annalen'', 77, 89–92 || Group theory. Proof that the invariants of a finite group are themselves finite, following the methods of David Hilbert. |- | 8 || 1915 || (Über ganze rationale Darstellung der Invarianten eines Systems von beliebig vielen Grundformen ) | ''Mathematische Annalen'', 77, 93–102 || Applies her earlier work on ''n''-forms.〔vdW, p. 102〕 |- | 9 || 1916 || (Die allgemeinsten Bereiche aus ganzen transzendenten Zahlen ) | ''Mathematische Annalen'', 77, 103–128 (corrig., 81, 30) || |- | 10 || 1916 || (Die Funktionalgleichungen der isomorphen Abbildung ) | ''Mathematische Annalen'', 77, 536–545 || |- | 11 || 1918 || (Gleichungen mit vorgeschriebener Gruppe ) | ''Mathematische Annalen'', 78, 221–229 (corrig., 81, 30) || Galois theory. Important paper on the inverse Galois problem — as assessed by B. L. van der Waerden in 1935, her work was "the most significant contribution made by anyone so far" to this still-unsolved problem. |- | 12 || 1918 || (Invarianten beliebiger Differentialausdrücke ) | ''Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Math.-phys. Klasse'', 1918, 38–44 || Differential invariants. Introduces the concept of a reduced system, in which some differential invariants are reduced to algebraic invariants. |- | 13 || 1918 || (Invariante Variationsprobleme ) | ''Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Math.-phys. Klasse'', 1918, 235–257 || Differential invariants. Seminal paper introducing Noether's theorems, which allow differential invariants to be developed from symmetries in the calculus of variations. |- | 14 || 1919 || (Die arithmetische Theorie der algebraischen Funktionen einer Veränderlichen in ihrer Beziehung zu den übrigen Theorien und zu der Zahlkörpertheorie ) | ''Jahresbericht der Deutschen Mathematiker-Vereinigung'', 28 (Abt. 1), 182–203 || |- | 15 || 1919 || (Die Endlichkeit des Systems der ganzzahligen Invarianten binärer Formen ) | ''Nachrichte der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Math.-phys. Klasse'', 1919, 138–156 || Algebraic invariants. Proof that the integral invariants of binary forms are themselves finite. Similar to publication #7, this paper is devoted to the research area of Hilbert. |- | 16 || 1920 || (Zur Reihenentwicklung in der Formentheorie ) | ''Mathematische Annalen'', 81, 25–30 || Another application of her work in publication #4 on the algebraic invariants of forms with ''n'' variables. |} 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Emmy Noether bibliography」の詳細全文を読む スポンサード リンク
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