Emmy Noether was initially interested in invariant theory. But how did she become interested in abstract algebra? And why did she become particularly interested in ring and ideal theory?
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6$\begingroup$ McTutor has Noether's biography, which quotes her own words on the subject:"Above all I am indebted to Mr E Fischer from whom I received the decisive impulse to study abstract algebra from an arithmetical viewpoint, and this remained the governing idea for all my later work." Fischer succeeded Gordan to the chair of mathematics in Erlangen in 1911, and Gordan's influence was responsible for her previous interest in the invariant theory. $\endgroup$– ConifoldCommented Nov 18, 2023 at 7:43
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1$\begingroup$ See MBW Tent, Emmy Noether: The Mother of Modern Algebra (2008) $\endgroup$– Mauro ALLEGRANZACommented Nov 20, 2023 at 10:13
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Ernst Fischer was hired by Erlangen in 1911. He is known to us today for his work in analysis (Riesz-Fischer theorem), but he worked on algebraic topics at Erlangen (and his thesis was on determinants). He influenced Noether's direction of work towards Hilbert's approach to studying polynomial rings, which had success in proving results of sweeping generality without tedious computations; think of Hilbert's basis theorem. Noether's thesis had hundreds of calculations in it and she never thought highly of this work. That experience perhaps made her more interested in a style of math that was more conceptual and less computational, which in her case turned out to be abstract algebra.
