#### 82 Citations

Prehistory
of the Concept
of Mathematical Structure: Isomorphism Between Group Theory, Crystallography,
and Philosophy

- Mathematics
- 2012

Formalization of Ring Theory in PVS

- Mathematics
- 2021

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 characterizations… Expand

Dedekind semidomains

- Mathematics
- 2019

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 a… Expand

Duality in Non-Abelian Algebra IV. Duality for groups and a universal isomorphism theorem

- Mathematics
- Advances in Mathematics
- 2019

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 more… Expand

Profinite Groups and Infinite Galois Extensions

- Mathematics
- 2019

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 closed… Expand

The History of Algebra’s Impact on the Philosophy of Mathematics

- Mathematics
- 2017

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 like… Expand

The Two Mathematical Careers of Emmy Noether

- 2017

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 understates… Expand