Emmy Noether bibliography
Emmy Noether was a German mathematician. This article lists the publications upon which her reputation is built (in part).
First epoch (1908–1919)
Index[1] | Year | Title and English translation[2] | Journal, volume, pages | Classification and notes | |
---|---|---|---|---|---|
1 | 1907 | Über die Bildung des Formensystems der ternären biquadratischen Form
| Sitzung Berichte der Physikal.-mediz. Sozietät in Erlangen, 39, 176–179 | Algebraic invariants. Preliminary 4-page report on her dissertation results. | |
2 | 1908 | Über die Bildung des Formensystems der ternären biquadratischen Form
| 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.[3] | |
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. |
Second epoch (1920–1926)
In the second epoch, Noether turned her attention to the theory of rings. With her paper Moduln in nichtkommutativen Bereichen, insbesondere aus Differential- und Differenzenausdrücken, Hermann Weyl states, "It is here for the first time that the Emmy Noether appears whom we all know, and who changed the face of algebra by her work."
Index[1] | Year | Title and English translation[2] | Journal, volume, pages | Classification and notes | |
---|---|---|---|---|---|
17 | 1920 | Moduln in nichtkommutativen Bereichen, insbesondere aus Differential- und Differenzenausdrücken
| 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
| 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
| 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
| Mathematische Annalen, 85, 26–33 | ||
21 | 1922 | Formale Variationsrechnung und Differentialinvarianten
| Encyklopädie der math. Wiss., III, 3, E, 68–71 (in: R. Weitzenböck, Differentialinvarianten) | ||
22 | 1923 | Zur Theorie der Polynomideale und Resultanten
| 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
| Jahresbericht der Deutschen Mathematiker-Vereinigung, 32, 177–184 | ||
24 | 1923 | Eliminationstheorie und allgemeine Idealtheorie
| 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
| 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
| Jahresbericht der Deutschen Mathematiker-Vereinigung, 33, 102 | ||
27 | 1925 | Hilbert Counts in the Theory of Ideals§ |
| Jahresbericht der Deutschen Mathematiker-Vereinigung, 34 (Abt. 2), 101 || |- | 28 || 1926 || Ableitung der Elementarteilertheorie aus der Gruppentheorie]
Derivation of the Theory of Elementary Divisors from Group Theory§ |
| Jahresbericht der Deutschen Mathematiker-Vereinigung, 34 (Abt. 2), 104 || |- | 29 || 1925 || Gruppencharaktere und Idealtheorie
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. |}
Third epoch (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
| 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
| Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1927, 221–228 | Group representations, modules and ideals. Written with R. 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
| 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
| 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
| Rec. Soc. Math. Moscou, 36, 65–72 | ||
37 | 1929 |
| Jahresbericht der Deutschen Mathematiker-Vereinigung, 39 (Abt. 2), 17 | ||
38 | 1932 | Normalbasis bei Körpern ohne höhere Verzweigung
| Journal für die reine und angewandte Mathematik, 167, 147–152 | ||
39 | 1932 | Beweis eines Hauptsatzes in der Theorie der Algebren
| Journal für die reine und angewandte Mathematik, 167, 399–404 | Written with R. Brauer and H. Hasse. | |
40 | 1932 | Hyperkomplexe Systeme in ihren Beziehungen zur kommutativen Algebra und zur Zahlentheorie
| Verhandl. Internat. Math. Kongress Zürich, 1, 189–194 | ||
41 | 1933 | Nichtkommutative Algebren
| Mathematische Zeitschrift, 37, 514–541 | ||
42 | 1933 | Der Hauptgeschlechtsatz für relativ-galoissche Zahlkörper
| Mathematische Annalen, 108, 411–419 | ||
43 | 1934 | Zerfallende verschränkte Produkte und ihre Maximalordnungen, Exposés mathématiques publiés à la mémoire de J. Herbrand IV
| Actualités scient. et industr., 148 | ||
44 | 1950 | Idealdifferentiation und Differente
| Journal für die reine und angewandte Mathematik, 188, 1–21 |
References
- ^ a b c These Index numbers are used for cross-referencing in the "Classification and notes" column. The numbers are taken from the Brewer and Smith reference cited in the Bibliography, pp. 175–177.
- ^ a b c The translations shown in black are taken from the Kimberling source. Unofficial translations are given in purple font.
- ^ vdW, p. 102
Bibliography
- Brewer JW, Smith MK, eds. (1981). Emmy Noether: A Tribute to Her Life and Work. New York: Marcel Dekker. ISBN 0-8247-1550-0.
- Dick A (1970). Emmy Noether 1882–1935 ((Beihft Nr. 13 zur Zeitschrift Elemente der Mathematik) ed.). Basel: Birkhäuser Verlag. pp. 40–42.
- Kimberling, Clark (1981), "Emmy Noether and Her Influence", in James W. Brewer; Martha K. Smith (eds.), Emmy Noether: A Tribute to Her Life and Work, New York: Marcel Dekker, Inc., pp. 3–61, ISBN 0-8247-1550-0.
- Noether, Emmy (1983), Jacobson, Nathan (ed.), Gesammelte Abhandlungen (Collected Works), Berlin, New York: Springer-Verlag, pp. 773–775, ISBN 978-3-540-11504-5, MR 0703862
External links
- List of Emmy Noether's publications by Dr. Cordula Tollmien
- List of Emmy Noether's publications in the eulogy by Bartel Leendert van der Waerden
- Partial listing of important works at the Contributions of 20th century Women to Physics at UCLA
- MacTutor biography of Emmy Noether