gh-37137: some details in infinity "ring"
    
some typing annotations, and using the base class `CommutativeRing`

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #37137
Reported by: Frédéric Chapoton
Reviewer(s): Frédéric Chapoton, Travis Scrimshaw

Author: Release Manager