Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern

  title={Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenk{\"o}rpern},
  author={Emmy Noether},
  journal={Mathematische Annalen},
On a classical theorem of Noether in ideal theory.
Formalization of Ring Theory in PVS
This paper presents a PVS development of relevant results of the theory of rings. The PVS theory includes complete proofs of the three classical isomorphism theorems for rings, and characterizationsExpand
Dedekind semidomains
We define Dedekind semidomains as semirings in which each nonzero fractional ideal is invertible. Then we find some equivalent condition for semirings to being Dedekind. For example, we prove that aExpand
Duality in Non-Abelian Algebra IV. Duality for groups and a universal isomorphism theorem
Abelian categories provide a self-dual axiomatic context for establishing homomorphism theorems (such as the isomorphism theorems and homological diagram lemmas) for abelian groups, and moreExpand
Profinite Groups and Infinite Galois Extensions
In the 1930’s Wolfgang Krull extended the fundamental theorem of Galois theory to infinite Galois extension via introducing a topology on the Galois group. This gave a correspondence between closedExpand
The History of Algebra’s Impact on the Philosophy of Mathematics
Structuralism in the philosophy of mathematics encompasses a range of views, many of which see structures, such as the natural numbers, as the proper objects of mathematics, rather than objects likeExpand
The Two Mathematical Careers of Emmy Noether
The received view of Emmy Noether as the champion of David Hilbert’s new style of algebra is not false (as you can see from the fact that Hermann Weyl urged this view). But it seriously understatesExpand