Mathematics

Noether, Amalie Emmy | Der Diskriminantensatz für die Ordnungen eines algebraischen Zahl- oder Funktionenkörpers

  • First edition, the uncommon offprint issue, of an important paper developing the theory of ideals in commutative ring theory, utilising ascending chain conditions, part of the author’s development of what is now known as modern abstract algebra.

    Described by Albert Einstein as “the most significant creative mathematical genius thus far produced since the higher education of women began” (letter to the editor, the New York Times, May 4th, 1935), Emmy Noether (1882-1935) was born into a family of distinguished German-Jewish mathematicians and scientists. She studied mathematics at the University of Erlangen and was awarded her doctorate in 1907 for her dissertation on algebraic invariants. Unable to obtain a paid position, Noether worked without compensation at Erlangen and then Göttingen before receiving the title “unofficial associate professor” and a small salary in 1922. When the Nazis came to power she accepted a position at Bryn Mawr, “partly because of its tradition of eminent female mathematicians”, and remained there until her death in 1935 (Ogilvie, Biographical Dictionary of Women in Science, p. 949).

    Mathematician Hermann Weyl divided Noether’s career into three distinct periods: relative dependancy (1908-1919), the theory of ideals (1920-1926) and noncommunicative algebras (1927-1935) “Noether saw the creation of general abstract algebra as her life’s work. Instead of classical algebra with real numbers, or complex numbers, and polynomials using them, she would study any system satisfying abstract rules such as the ring axioms or the group axioms. Concrete examples include the ring of all algebraic functions defined on a space (such as a sphere), and the group of all symmetries of a given space. She largely created the now-standard style of abstract algebra” (McLarty, The Princeton Companion to Mathematics, VI.76, pp 800-801). “Her work in abstract algebra, in which she concentrated on formal properties such as associativity, commutativity, and distributivity, has inspired so many successors that mathematicians speak of the ‘Noether school’ of mathematics” (Ogilvie).

  • ...[Offprint from] Journal für die Reine und Angewandte Mathmatik. Sonderabdruck aus Bd. 157. (Jubiläumsband I.) 30th March, 1926. Berlin: Walter de Gruyter & Co., [1927].

    Quarto. Wire-stitched, marbled backstrip. Pencilled notes to the upper leaf and on equations within the margins. Residue of ticket removal from the upper leaf. A little worn, vertical and horizontal creases from folding, a short closed tear in the horizontal fold of the first leaf has been repaired with tape on the verso, a few other small chips and splits to the first and last leaves. Very good condition.