There is an outstanding female mathematician who is recognized as one of the founders of abstract algebra and is known as the "queen of algebra". She is emmy noether,1born in Hellem, Germany on March 23rd, 882. 1900 entered the University of Herun Root, and 1907 received her doctorate under the guidance of mathematician Gordan. Noether's work has an important influence on the development of algebraic topology, algebraic number theory and algebraic geometry. In 1907- 19 19, she mainly studies algebraic invariants and differential invariants. In her doctoral thesis, she gave a set of invariants of ternary quartic form. It also solves the existence problem of finite rational basis in rational function domain. The constructive proof that the invariants of finite groups have finite bases is given. She uses direct differentiation instead of elimination to generate differential invariants. In her inaugural thesis at the University of G? ttingen, she discussed the invariants under continuous groups (Lie groups) and gave Noether theorem, which linked symmetry, invariance and conservation laws in physics. From 1920 to 1927, she mainly studied commutative algebra and commutative arithmetic. After 19 16, she began to transition from classical algebra to abstract algebra. In 1920, she introduced the concepts of "left module" and "right module". Written in1921 An axiomatic characterization of Dedekind ring is given, and the necessary and sufficient conditions for the unique decomposition theorem of prime ideal factors are pointed out. Nott's theory is also the system theory of "ring" and "ideal" in modern mathematics. It is generally believed that the time of abstract algebra is 1926. Since then, the research object of algebra has changed from studying the calculation and distribution of algebraic equations to studying the algebraic operation rules and various algebraic structures of numbers, words and more general elements, thus completing the essential transformation from classical algebra to abstract algebra. Nott is well-deserved as one of the founders of abstract algebra. Noether studied noncommutative algebra and noncommutative arithmetic in 1927- 1935. She unified representation theory, idealism theory and module theory on the basis of so-called "hypercomplex system", that is, algebra. Later, the concept of cross product was introduced and used to determine the Boolean group of finite dimensional Galois extension. Finally, the proof of the main theorem of algebra is introduced. The central divisible algebra in algebraic number field is cyclic algebra.