Emmy Noether

Female mathematician having shaped commutative algebra and related technology (or vice versa) for decades.

• 1882-1935. Born in Erlangen, Bavaria. Her last two years were in the USA in Bryn Mawr and Princeton. She was the daughter of Max Noether.
• She established the primary decomposition for commutative Noetherian rings in her 1921 paper Idealtheorie in Ringbereichen. Math. Ann. 83 24-66.
• (x²,xy)=(x²) intersect (x,y) is an example of a primary decomposition in the polynomial ring k[x,y].
• Noetherian rings are named after her. A ring is right Noetherian if it has the ascending chain condition on right ideals. That is, every ascending chain of right ideals eventually stablises.
• She also has a lunar crater named after her.
• Early in her career Nöther had to fight against prejudice to teach at Göttingen. Hilbert helped her by announcing her lectures under his name.
• As a Jew she has dismissed from Göttingen in 1933. She left for the USA, dying a couple of years later.