TITLE: Example of the non-commutative ring with the set of units are commutative
QUESTION [5 upvotes]: I was looking for an Example of the non-commutative ring with the set of units are commutative. it will be a great help. Thanks in advance.

REPLY [2 votes]: For any monoid $M$ with no units and trivial center, and any commutative ring $R$, the monoid ring $R[M]$ will have the same units as $R$.