Abstract
Emmy Noether is universally regarded as the greatest woman mathematician so far. In this chapter, we look at some of her work in the creation of modern algebra.
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- 1.
She eventually obtained a modest salary.
- 2.
As was her brother Fritz, a physicist, who left for the Soviet Union where he was eventually murdered in the purges of the 1930s.
- 3.
For this Noether , in an account written by someone who does know all three Noether s, see (Kosman-Schwarzbach 2011).
- 4.
Fraenkel added two further definitions to assist him in obtaining factorisation theorems; see (Corry 1996, p. 210).
- 5.
There is an English translation of this paper by Daniel Berlyne, who took this course for pleasure in 2013–14; see arXiv:1401.2577 [math.RA].
- 6.
A ring R has zero divisors a, b ∈ R if a ≠ 0, b ≠ 0, ab = 0.
- 7.
As Corry points out (1996, p. 239), Noether ’s use of the ascending chain condition is much more explicit and central in her paper (1926), which unfortunately I cannot consider here.
References
Corry, L.: Modern algebra and the rise of mathematical structures. Science Networks. Historical Studies, vol. 17, 2nd edn. 2004. Birkhäuser, Basel (1996)
Fraenkel, A.: Über die Teiler der Null und die Zerlegung von Ringen. J. Math. 145, 139–176 (1914)
Koreuber, M.: Emmy Noether, die Noether-Schule und die moderne Algebra. Zur Geschichte einer kulturellen Bewegung. Springer, Berlin (2015)
Kosman-Schwarzbach, Y.: The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century: Invariance and Conservation Laws in the 20th Century, B. Schwarzbach (transl.). Springer, Berlin (2011)
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Gray, J. (2018). Emmy Noether. In: A History of Abstract Algebra. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-94773-0_28
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