Emmy Noether (1882 — 1935) est une mathématicienne allemande spécialiste de l'algèbre. Cet article est une liste de publications qui ont fait renommée.
| Index | Année | Titre, traduction en anglais et en français. | Revue, volume, pages | Classification et notes |
| 1 | 1907 | Über die Bildung des Formensystems der ternären biquadratischen Form | On Complete Systems of Invariants for Ternary Biquadratic Forms | | Construction du système de formes de la forme ternaire biquadratique | | Sitzung Berichte der Physikal.-mediz. Sozietät in Erlangen, 39, 176–179 | Invariants algébriques. Rapport préliminaire de quatre pages sur sa thèse. |
| 2 | 1908 | Über die Bildung des Formensystems der ternären biquadratischen Form | On Complete Systems of Invariants for Ternary Biquadratic Forms | | Construction du système de formes de la forme ternaire biquadratique | | Journal für die reine und angewandte Mathematik, 134, 23–90 + 2 tables | Invariants algébriques. Thèse, comprenant les calculs de 331 invariants ternaires. |
| 3 | 1910 | Zur Invariantentheorie der Formen von n Variabeln | On the Theory of Invariants for Forms of n Variables§ | | 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 | On the Theory of Invariants for Forms of n Variables§ | | 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 and . |
| 5 | 1913 | Rationale Funktionenkörper | Rational Function Fields§ | | Jahresbericht der Deutschen Mathematiker-Vereinigung, 22, 316–319 | Field theory. See the following paper. |
| 6 | 1915 | Körper und Systeme rationaler Funktionen | Fields and Systems of Rational Functions | | 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 on the inverse Galois problem. |
| 7 | 1915 | Der Endlichkeitssatz der Invarianten endlicher Gruppen | The Finiteness Theorem for Invariants of Finite Groups | | 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 | On an Integral Rational Representation of the Invariants of a System of Arbitrarily Many Basis Forms§ | | Mathematische Annalen, 77, 93–102 | Applies her earlier work on n-forms. |
| 9 | 1916 | Die allgemeinsten Bereiche aus ganzen transzendenten Zahlen | The Most General Domains of Completely Transcendental Numbers | | Mathematische Annalen, 77, 103–128 (corrig., 81, 30) | |
| 10 | 1916 | Die Funktionalgleichungen der isomorphen Abbildung | Functional Equations of the Isomorphic Mapping | | Mathematische Annalen, 77, 536–545 | |
| 11 | 1918 | Gleichungen mit vorgeschriebener Gruppe | Equations with Prescribed Group | | 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 | Invariants of Arbitrary Differential Expressions§ | | 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 | Invariant Variation Problems | | 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 | The Arithmetic Theory of Algebraic Functions of One Variable in its Relationship to the Other Theories and to Number Field Theory§ | | Jahresbericht der Deutschen Mathematiker-Vereinigung, 28 (Abt. 1), 182–203 | |
| 15 | 1919 | Die Endlichkeit des Systems der ganzzahligen Invarianten binärer Formen | A Proof of Finiteness for Integral Binary Invariants | | 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 , this paper is devoted to the research area of Hilbert. |
| 16 | 1920 | Zur Reihenentwicklung in der Formentheorie | On Series Expansions in the Theory of Forms§ | | Mathematische Annalen, 81, 25–30 | Another application of her work in publication on the algebraic invariants of forms with n variables. |
