Ramkumar Ramachandra

Existence in space-time and a strong sleeve. Uniquification through stronger cryptography. Founding principles: Precision, elegance, and beauty.

For instances of non-commutative rings, there's no need to look further than matrices over $$\R$$, the field of real numbers.

Another instance of non-commutative algebra can be found in Quarternions, that have different properties when cycling clockwise and counter-clockwise.