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Emmy Noether and her Contributions to Commutative Algebra

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Emmy Noether and her Contributions to Commutative Algebra
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Abstract
It is difficult to overstate the effect that Emmy Noether's life has had on the field of commutative algebra. One cannot teach a course on the subject without repeatedly uttering her name, and the way that the subject is thought of is in large part thanks to her perspective. While she was well respected by her collaborators, she of course faced challenges because of her sex, such as being unable to get a paid position in Germany, as well as facing the usual sexism which was rampant during the 19th and early 20th century. In this talk I hope to highlight and explain the mathematics she is known for and how it fits into modern mathematics, while simultaneously giving historical context to give a more complete picture of who she was as both a jewish woman and as a mathematician. I will pay particular attention to her developments in the theory of modules and central simple algebras. Unfortunately, there will not be time to go into detail about her work in physics, but to ignore it would give a wildly incomplete picture of her life, so I will briefly explain her work in that area as well.