Can you please provide references how non-communative ring theory works in mathematics outside non-commutative ring theory?
I am interested in applications in the following fields: topology, geometry, algebraic geometry, invariant theory, algebraic number theory, combinatorics, combinatorial geometry, convex polyhedra, K-theory, Lie theory, PDE.
I am especially interested in those (concrete) applications that allows:
prove existence of something
I do not expect detailed answers, this is just reference request. However, you are welcome to provide deep answers that I will understand in several years from now. Concrete computations, books and reviews are highly appreciated.
Thanks for your time!
Please continue to provide answers, I will be happy to upvote every relevant answer!