Peter Roquette on Emmy Noether

“Emmy Noether's creative power was directed quite generally towards the clarification of mathematical structures and concepts through abstraction, which means leaving all unnecessary entities and properties aside and concentrating on the essentials. Her basic work in this direction can be subsumed under algebra, but her methods eventually penetrated all mathematical fields, including number theory and topology.”

“We may assume that Emmy Noether studied, like Weyl, all of Hilbert's papers, at least those which were concerned with algebra or arithmetic. In particular she would have read the paper ["Über die Theorie der algebraischen Formen" (1890)] where Hilbert proved that every ideal in a polynomial ring is finitely generated; in her famous later paper ["Idealtheorie in Ringbereichen" (1921)] she considered arbitrary rings with this property, which today are called "Noetherian rings". ...Hilbert's Zahlbericht too was... studied; it was the standard text which every young mathematician of that time read... to learn algebraic number theory. ...Steinitz' great paper "Algebraische Theorie der Körper"...marks the start of abstract field theory... [and] is often mentioned in her later publications, as the basis for her abstract viewpoint of algebra.”