In the book "Abstract Algebra" by Dummit, the definition of irreducible element in an integral domain $R$ goes like this.
Suppose $r\in R$ is nonzero and is not a unit. Then $r$ is called irreducible in $R$ if whenever $r=ab$ with $a,b\in R$, at least one of $a$ or $b$ must be a unit in $R$. Otherwise $r$ is said to be reducible...
My questions are
why we don't consider the units to be irreducible?
In the definition above, I get confused by the definition of reducible elements: namely, the units are reducible or not?
Thanks in advance..