Question
This mathematician’s normalization lemma asserts that all finitely generated algebras over a field k can be represented as finitely generated modules over a polynomial ring of k. For 10 points each:
[10h] Identify this mathematician whose namesake rings satisfy the ascending chain condition on ideals.
ANSWER: Emmy Noether (“NUR-tuh”) [or Amalie Emmy Noether; accept Noetherian rings or Noether’s normalization lemma]
[10m] Noether’s normalization lemma can be used in a simple proof of this mathematician’s Nullstellensatz (“NOOL-shtell-in-zotts”). This man names a class of function spaces used in quantum mechanics and also devised a program aiming for a finite set of axioms for all of mathematics.
ANSWER: David Hilbert [accept Hilbert space or Hilbert’s Nullstellensatz or Hilbert’s program]
[10e] Noether and Hilbert’s works in commutative algebra were early contributions to this subject’s “algebraic” branch. Its formulation in Euclid’s Elements, which includes the parallel postulate, is consistent and complete.
ANSWER: geometry [accept algebraic geometry or Euclidean geometry]
<Other Science>
Summary
| 2023 ACF Winter @ Columbia | 11/11/2023 | Y | 9 | 14.44 | 89% | 33% | 22% |
Data
| Princeton A | Bard A | 0 | 0 | 10 | 10 |
| Columbia A | Rutgers B | 0 | 10 | 10 | 20 |
| Cornell C | Princeton B | 0 | 0 | 10 | 10 |
| NYU A | Columbia C | 0 | 0 | 10 | 10 |
| Penn A | Haverford | 10 | 10 | 10 | 30 |
| Rutgers A | NYU B | 10 | 10 | 10 | 30 |
| Penn B | Yale A | 0 | 0 | 10 | 10 |
| Rowan A | Yale B | 0 | 0 | 0 | 0 |
| Yale C | Vassar | 0 | 0 | 10 | 10 |