One way to prove another of his theorems hinges on proving Zariski's lemma; that theorem uses two bijective maps which are inverses of each other to show a correspondence between affine varieties(*) and radical ideals in a polynomial ring and is a foundational result of algebraic geometry.
One famous result named for him states that if G is the cyclic Galois group of a finite extension K over F with generator beta, and u is an element in K with a relative norm of 1, then there exists v such that u is equal to beta of v, divided by v. That theorem, actually discovered by Ernst Kummer, was the 90th in a volume that he was to co-author with Minkowski, though Minkowski ended up not contributing. One way to prove another of his theorems hinges on proving Zariski's lemma; that theorem uses two bijective maps which are inverses of each other to show a correspondence between affine varieties(*) and radical ideals in a polynomial ring and is a foundational result of algebraic geometry. Another of his theorems states that if R is a Noetherian ring, then the polynomial ring over R is also Noetherian. These results are respectively his Theorem 90, his Nullstellensatz, and his basis theorem. For 10 points, name this former University of Göttingen professor who at the 1900 International Congress of Mathematicians presented a list of 23 important unsolved problems.
One famous result named for him states that if G is the cyclic Galois group of a finite extension K over F with generator beta, and u is an element in K with a relative norm of 1, then there exists v such that u is equal to beta of v, divided by v. That theorem, actually discovered by Ernst Kummer, was the 90th in a volume that he was to co-author with Minkowski, though Minkowski ended up not contributing.
David Hilbert