List of publications by Emmy Noether

Emmy Noether is counted among the greatest mathematicians of all time. 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.
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3 || 1910 || [http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=244194 Zur Invariantentheorie der Formen von "n" Variabeln]
"Jahresbericht der Deutschen Mathematiker-Vereinigung", 22, 316–319 || Field theory. See the following paper.
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6 || 1915 || [http://www.digizeitschriften.de/index.php?id=loader&tx_jkDigiTools_pi1%5BIDDOC%5D=362546 Körper und Systeme rationaler Funktionen]
"Mathematische Annalen", 77, 93–102 || Applies her earlier work on "n"-forms. [vdW, p. 102]
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9 || 1916 || [http://www.digizeitschriften.de/index.php?id=loader&tx_jkDigiTools_pi1%5BIDDOC%5D=461160 Die allgemeinsten Bereiche aus ganzen transzendenten Zahlen]
"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.
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12 || 1918 || [http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=63702 Invarianten beliebiger Differentialausdrücke]
"Jahresbericht der Deutschen Mathematiker-Vereinigung", 28 (Abt. 1), 182–203 ||
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15 || 1919 || [http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=63745 Die Endlichkeit des Systems der ganzzahligen Invarianten binärer Formen]

econd 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."

"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.
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19 || 1921 || [http://www.digizeitschriften.de/index.php?id=loader&tx_jkDigiTools_pi1%5BIDDOC%5D=362701 Idealtheorie in Ringbereichen]
"Encyklopädie der math. Wiss.", III, 3, E, 68–71 (in: R. Weitzenböck, "Differentialinvarianten") ||
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22 || 1923 || [http://www.digizeitschriften.de/index.php?id=loader&tx_jkDigiTools_pi1%5BIDDOC%5D=362882 Zur Theorie der Polynomideale und Resultanten]
"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.
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25 || 1924 || [http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=248880 Eliminationstheorie und Idealtheorie]
"Jahresbericht der Deutschen Mathematiker-Vereinigung", 34 (Abt. 2), 101 ||
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28 || 1926 || [http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=248861 Ableitung der Elementarteilertheorie aus der Gruppentheorie] [Scroll forward to page 104.]
"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.
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31 || 1926 || [http://www.digizeitschriften.de/index.php?id=loader&tx_jkDigiTools_pi1%5BIDDOC%5D=363121 Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern]
"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.
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34 || 1928 || Hyperkomplexe Größen und Darstellungstheorie, in arithmetischer Auffassung
"Rec. Soc. Math. Moscou", 36, 65–72 ||
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37 || 1929 || Idealdifferentiation und Differente
"Journal für die reine und angewandte Mathematik", 167, 399–404 || Written with R. Brauer and H. Hasse.
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40 || 1932 || Hyperkomplexe Systeme in ihren Beziehungen zur kommutativen Algebra und zur Zahlentheorie
"Mathematische Annalen", 108, 411–419 ||
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43 || 1934 || Zerfallende verschränkte Produkte und ihre Maximalordnungen, Exposés mathématiques publiés à la mémoire de J. Herbrand IV

References

Bibliography

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*Citation | last1=Noether | first1=Emmy | author1-link=Emmy Noether | editor1-last=Jacobson | editor1-first=Nathan | editor1-link=Nathan Jacobson | title=Gesammelte Abhandlungen (Collected Works)| publisher=Springer-Verlag | location=Berlin, New York | isbn=978-3-540-11504-5 | id=MathSciNet | id = 703862 | year=1983| pages = 773–775 | url = http://books.google.com/books?id=bsm5lmprAQQC

External links

* [http://physikerinnen.de/noetherpublikationen.html List of Emmy Noether's publications by Dr. Cordula Tollmien]

* [http://www.rzuser.uni-heidelberg.de/~ci3/hasse-noether/noether-vdw.pdf List of Emmy Noether's publications in the eulogy] by Bartel Leendert van der Waerden

* [http://cwp.library.ucla.edu/Phase2/Noether,[e-mail] Partial listing of important works] at the [http://cwp.library.ucla.edu/exp.html Contributions of 20th century Women to Physics] at UCLA

* [http://www-history.mcs.st-andrews.ac.uk/history/Biographies/Noether_Emmy.html MacTutor biography of Emmy Noether]