Light PhD Seminar: Prehistory of Commutative Algebra. Noether, Hilbert and Noether.

Title: Prehistory of Commutative Algebra. Noether, Hilbert and Noether.

Abstract:
Emmy Noether's "Idealtheorie", published in 1920, planted the seed of Commutative Algebra as we know it today. With the language of the recently established "theory of rings", she was able to generalise several important results of the theory of polynomials by capturing the essential property that made them work: the ascending chain condition.

Behind these far-reaching results lies the history of theorems that are fundamental to today's Commutative Algebra and Algebraic Geometry, such as Hilbert's Basis theorem, Hilbert's Nullstellensatz or Lasker's Primary decomposition, which find their roots in the second half of the 19th century.

In this talk, we will discuss this period of mathematical history starting from two major problems of Algebra and Geometry of the 19th century, Gordan's problem and Noether's problem. Remarkably, the only requirements for our discussion will be knowing what a polynomial is.