- Liste des publications d'Emmy Noether
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Emmy Noether (1882 — 1935) est une mathématicienne allemande spécialiste de l'algèbre. Cet article est une liste des publications qui ont fait sa renommée.
Sommaire
Première époque (1908–1919)
Index[1] Année Titre, traduction en anglais[2] 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[3] 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 #8 and #16. 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 #11 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[4]. 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 #7, 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 #4 on the algebraic invariants of forms with n variables. Deuxième époque (1920–1926)
Dans la deuxième période de sa carrière, Noether se tourne vers la théorie des annaux. À propos de son article Moduln in nichtkommutativen Bereichen, insbesondere aus Differential- und Differenzenausdrücken, Hermann Weyl affirme : « C'est là qu'apparaît pour la première fois l'Emmy Noether que nous connaissons tous, celle dont les recherches ont changé la face de l'algèbre. »
Index[1] Année Titre et traductions en anglais[2] et français Revue, volume, pages Classification et notes 17 1920 Moduln in nichtkommutativen Bereichen, insbesondere aus Differential- und Differenzenausdrücken Modules in Non-commutative Domains, especially Those Composed of Differential and Difference Expressions§ Mathematische Zeitschrift, 8, 1–35 Ideals and modules. Written with W. Schmeidler. Seminal paper that introduces the concepts of left and right ideals, and develops various ideas of modules: direct sums and intersections, residue class modules and isomorphy of modules. First use of the exchange method for proving uniqueness, and first representation of modules as intersections obeying an ascending chain condition. 18 1921 Über eine Arbeit des im Kriege gefallenen K. Hentzelt zur Eliminationstheorie[5] On a Work on Elimination Theory by K. Hentzelt, who Fell in the War§ Jahresbericht der Deutschen Mathematiker-Vereinigung, 30 (Abt. 2), 101 Elimination theory. Preliminary report of the dissertation of Kurt Hentzelt, who died during World War I. The full description of Hentzelt's work came in publication #22. 19 1921 Idealtheorie in Ringbereichen The Theory of Ideals in Ring Domains§ Mathematische Annalen, 83, 24–66 Ideals. Considered by many mathematicians to be Noether's most important paper. In it, Noether shows the equivalence of the ascending chain condition with previous concepts such as Hilbert's theorem of a finite ideal basis. She also shows that any ideal that satisfies this condition can be represented as an intersection of primary ideals, which are a generalization of the einartiges Ideal defined by Richard Dedekind. Noether also defines irreducible ideals and proves four uniqueness theorems by the exchange method, as in publication #17. 20 1922 Ein algebraisches Kriterium für absolute Irreduzibilität An Algebraic Criterion for Absolute Irreducibility§ Mathematische Annalen, 85, 26–33 21 1922 Formale Variationsrechnung und Differentialinvarianten Formal Calculus of Variations and Differential Invariants§ Encyklopädie der math. Wiss., III, 3, E, 68–71 (in: R. Weitzenböck, Differentialinvarianten) 22 1923 Zur Theorie der Polynomideale und Resultanten On the Theory of Polynomial Ideals and Resultants§ Mathematische Annalen, 88, 53–79 Elimination theory. Based on the dissertation of Kurt Hentzelt, who died before this paper was presented. In this work, and in publications #24 and #25, Noether subsumes elimination theory within her general theory of ideals. 23 1923 Algebraische und Differentialinvarianten Algebraic and Differential Invariants§ Jahresbericht der Deutschen Mathematiker-Vereinigung, 32, 177–184 24 1923 Eliminationstheorie und allgemeine Idealtheorie Elimination Theory and the General Ideal Theory§ Mathematische Annalen, 90, 229–261 Elimination theory. Based on the dissertation of Kurt Hentzelt, who died before this paper was presented. In this work, and in publications #24 and #25, Noether subsumes elimination theory within her general theory of ideals. 25 1924 Eliminationstheorie und Idealtheorie Elimination Theory and Ideal Theory§ Jahresbericht der Deutschen Mathematiker-Vereinigung, 33, 116–120 Elimination theory. Based on the dissertation of Kurt Hentzelt, who died before this paper was presented. In this work, and in publications #24 and #25, Noether subsumes elimination theory within her general theory of ideals. She developed a final proof during a lecture in 1923/1924. When her colleague van der Waerden developed the same proof independently (but working from her publications), Noether allowed him to publish. 26 1924 Abstrakter Aufbau der Idealtheorie im algebraischen Zahlkörper[6] Abstract Structure of the Theory of Ideals in Algebraic Number Fields§ Jahresbericht der Deutschen Mathematiker-Vereinigung, 33, 102 27 1925 Hilbertsche Anzahlen in der Idealtheorie[5] Hilbert Counts in the Theory of Ideals§ Jahresbericht der Deutschen Mathematiker-Vereinigung, 34 (Abt. 2), 101 28 1926 Ableitung der Elementarteilertheorie aus der Gruppentheorie[7] Derivation of the Theory of Elementary Divisors from Group Theory§ Jahresbericht der Deutschen Mathematiker-Vereinigung, 34 (Abt. 2), 104 29 1925 Gruppencharaktere und Idealtheorie[8] Group Characters and the Theory of Ideals§ Jahresbericht der Deutschen Mathematiker-Vereinigung, 34 (Abt. 2), 144 Group representations, modules and ideals. First of four papers showing the close connection between these three subjects. See also publications #32, #33, and #35. 30 1926 Der Endlichkeitssatz der Invarianten endlicher linearer Gruppen der Charakteristik p Proof of the Finiteness of the Invariants of Finite Linear Groups of Characteristic p§ Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Math.-phys. Klasse, 1926, 28–35 By applying ascending and descending chain conditions to finite extensions of a ring, Noether shows that the algebraic invariants of a finite group are finitely generated even in positive characteristic. 31 1926 Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern Abstract Structure of the Theory of Ideals in Algebraic Number Fields and Function Fields§ Mathematische Annalen, 96, 26–61 Ideals. Seminal paper in which Noether determined the minimal set of conditions required that a primary ideal be representable as a power of prime ideals, as Richard Dedekind had done for algebraic numbers. Three conditions were required: an ascending chain condition, a dimension condition, and the condition that the ring be integrally closed. Troisième époque (1927–1935)
In the third epoch, Emmy Noether focused on non-commutative algebras, and unified much earlier work on the representation theory of groups.
Index[1] Year Title and English translation[2] Journal, volume, pages Classification and notes 32 1927 Der Diskriminantensatz für die Ordnungen eines algebraischen Zahl- oder Funktionenkörpers The Discriminant theorem for the Orders of an Algebraic Number Field or Function Field§ Journal für die reine und angewandte Mathematik, 157, 82–104 Group representations, modules and ideals. Second of four papers showing the close connection between these three subjects. See also publications #29, #33, and #35. 33 1927 Über minimale Zerfällungskörper irreduzibler Darstellungen On the Minimum Splitting Fields of Irreducible Representations§ Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1927, 221–228 Group representations, modules and ideals. Written with Richard Brauer. Third of four papers showing the close connection between these three subjects. See also publications #29, #32, and #35. This paper shows that the splitting fields of a division algebra are embedded in the algebra itself; the splitting fields are maximal commutative subfields either over the algebra, or over a full matrix ring over the algebra. 34 1928 Hyperkomplexe Größen und Darstellungstheorie, in arithmetischer Auffassung Hypercomplex Quantities and the Theory of Representations, from an Arithmetic Perspective§ Atti Congresso Bologna, 2, 71–73 Group representations, modules and ideals. Synopsis of her papers showing the close connection between these three subjects. See also publications #29, #32, #33, and #35. 35 1929 Hyperkomplexe Größen und Darstellungstheorie Hypercomplex Quantities and the Theory of Representations Mathematische Zeitschrift, 30, 641–692 Group representations, modules and ideals. Final paper of four showing the close connection between these three subjects. See also publications #29, #32, and #33. 36 1929 Über Maximalbereiche von ganzzahligen Funktionen On the Maximal Domains of Integral Functions§ Rec. Soc. Math. Moscou, 36, 65–72 37 1929 Differents and Ideal Differentiation§ Jahresbericht der Deutschen Mathematiker-Vereinigung, 39 (Abt. 2), 17 38 1932 Normalbasis bei Körpern ohne höhere Verzweigung Normal Basis in Fields without Higher Ramification§ Journal für die reine und angewandte Mathematik, 167, 147–152 39 1932 Beweis eines Hauptsatzes in der Theorie der Algebren Proof of a Main Theorem in the Theory of Algebras§ Journal für die reine und angewandte Mathematik, 167, 399–404 Written with Richard Brauer and Helmut Hasse. 40 1932 Hyperkomplexe Systeme in ihren Beziehungen zur kommutativen Algebra und zur Zahlentheorie Hypercomplex Systems in Their Relationship to Commutative Algebra and to Number Theory§ Verhandl. Internat. Math. Kongress Zürich 1, 189–194 41 1933 Nichtkommutative Algebren Non-commutative Algebras§ Mathematische Zeitschrift, 37, 514–541 42 1933 Der Hauptgeschlechtsatz für relativ-galoissche Zahlkörper The Principal Genus Theorem for Relatively Galois Fields of Numbers§ Mathematische Annalen, 108, 411–419 43 1934 Zerfallende verschränkte Produkte und ihre Maximalordnungen, Exposés mathématiques publiés à la mémoire de J. Herbrand IV Decomposing Crossed Products and Their Maximal Orders, in memory of J. Herbrand IV§ Actualités scient. et industr., 148 44 1950 Idealdifferentiation und Differente Differents and Ideal Differentiation§ Journal für die reine und angewandte Mathematik, 188, 1–21 References
- Cet index est utilisé pour les références croisées de la colonne Classification et notes. Les nombres sont issus de la référence Brewer et Smith citée en bibliographie, p. 175–177.
- Les traductions en anglais sont issues de Kimberling 1981.
- Traduction française issue de Dubreil 1986.
- vdW, p. 102
- Scroll forward to page 101.
- Scroll forward to page 102.
- Scroll forward to page 104.
- Scroll forward to page 144.
Bibliographie
- Paul Dubreil, « Emmy Noether », dans Cahiers du séminaire d'histoire des mathématiques, vol. 7, 1986, p. 15-27 [texte intégral]
- (en) Brewer JW, Smith MK, editors, Emmy Noether: A Tribute to Her Life and Work, New York, Marcel Dekker, 1981 (ISBN 978-0-8247-1550-2) (LCCN 81015203)
- (en) A. Dick, Emmy Noether 1882–1935, Basel, Birkhäuser Verlag, 1970, (Beihft Nr. 13 zur Zeitschrift Elemente der Mathematik)e éd., p. 40–42
- (en) Clark Kimberling (en), Emmy Noether: A Tribute to Her Life and Work, New York, Marcel Dekker, Inc., 1981 (ISBN 0-8247-1550-0), p. 3–61.
- (de) Emmy Noether, Gesammelte Abhandlungen (Collected Works), Berlin, New York, [[Springer-Verlag|Springer-Verlag]], 1983 (ISBN 978-3-540-11504-5) lire en ligne, p. 773–775, MR703862, œuvres rassemblées par Nathan Jacobson.
Liens externes
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