Avoid clashes with Mathlib

We have some declarations that can clash with Mathlib, like `Ring` and `Field`. We should either:
1. Use the definitions from Mathlib
2. Have them under our own namespaces
3. Rename them

Let's discuss

No files or tests are named. Start by locating the declarations that can clash with Mathlib, including Ring and Field, then review how the project currently organizes namespaces and definitions. Done means the project has chosen and applied a consistent approach that avoids those clashes.

Written by the indexing model from the issue text.