Let be a field, and an indeterminate. Let Define addition and multiplication in exactly the same as what we have

in the ordinary polynomialsbutwith this extra rule that for all So, for example

It's easy to see that is a ring with identity and that is commutative if and only if The ring is called the ring of Laurent polynomials with the twist A standard notation for is

or These rings are very important in ring theory and noncommutative algebraic geometry.

Problem: Find the center of

Warning:

Spoiler: