One Hundred Years of Commutative Rings

摘要

In October 1920, Emmy Noether submitted a paper entitled 'Idealtheorie in Ringbereichen' ('Ideal theory in ring domains') to the journal Mathematische Annalen 1. Its appearance in print the following year not only gave initial impetus to the theory of commutative rings, but also introduced a whole new outlook into mathematics. In this article, we briefly introduce Noether and her work, and describe how her 1921 paper fits into 20th-century mathematics~1.