Carl B. Boyer on Emmy Noether

“Dedekind's concern with algebra goes back to the 1850s, when he attended Dirichlet's lectures on number theory... and pursued intensive studies of Galois theory. ...[H]e developed an abstract treatment of elementary group theory at that time. After Dirichlet's death, Dedekind was charged with publishing Dirichlet's lectures on number theory. In appendices he presented... his ideal theory... The most axiomatic approach [1894]... was the one that especially influenced Emmy Noether and her school of algebraists in the 1920s.”

“With the appearance of Einstein's general theory of relativity, Hilbert turned to that subject, which also occupied his colleague Felix Klein. Interestingly, the most lasting mathematical contribution out of this effort came from an algebraist who had recently engaged in studies of differential invariants. This was Emmy Noether... the daughter of the algebraic geometer Max Noether, whom Hilbert and Klein brought to Göttingen to assist them in research. Her results were published in 1918; best known as "Noether's Theorem"...”

“Following [Abraham Fraenkel's] work, Emmy Noether, in 1921, transferred decomposition theorems for ideals in algebraic number fields to those for ideals in arbitrary rings. ...Noether and her students made other major contributions to ring theory before she turned to a treatment of finite group representations from an ideal-theoretic point of view. ...Chain conditions had been used since the days of Hölder and Dedekind but were brought to the fore in the 1921 paper [above]. Through Noether's influence... algebraic notions were linked to topology in the work of Heinz Hopf and Paul Alexandroff...”