#### Thesis Title

### Max Noether's Fundamental Theorem

#### Date of Graduation

Summer 2008

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

Richard Belshoff

#### Abstract

In this paper, we introduce and give proofs of some basic concepts of algebraic geometry leading up to a proof of Max Noether's Fundamental Theorem. This theorem states that under certain conditions, a curve H passing through the common intersections of two other curves F and G will be equal to a combination AF + BG of the two. For this reason, it is sometimes referred to as "the AF + BG theorem." Examples using Noether's Theorem are given, including several from Fulton's Algebraic Curves.

#### Keywords

Algebra, algebraic curve, algebraic geometry, Noether's theorem, polynomial

#### Subject Categories

Mathematics

#### Copyright

© Jacob Aaron Boswell

#### Recommended Citation

Boswell, Jacob Aaron, "Max Noether's Fundamental Theorem" (2008). *MSU Graduate Theses*. 1628.

https://bearworks.missouristate.edu/theses/1628

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