# Untying knots in 4D and Wedderburn's Theorem

## TL;DR

This paper demonstrates that Wedderburn's Theorem on finite division rings implies all knots and links in smooth 4D manifolds are trivial, revealing a deep connection between algebra and topology.

## Contribution

It establishes a novel link between algebraic structures and 4-dimensional topology by deriving topological triviality from algebraic properties.

## Key findings

- All knots and links in smooth 4D manifolds are trivial.
- Wedderburn's Theorem implies topological triviality in 4D.
- Connects algebraic theorems with topological properties.

## Abstract

It is proved that the Wedderburn Theorem on finite division rings implies that all knots and links in the smooth 4-dimensional manifolds are trivial.