Definition: Let R be an integral domain. A nonzero, nonunit element r in R is said to be irreducible if whenever r=ab, then a is a unit or b is a unit. My question is are units considered irreducible. This how I understand it, Let v in R be a unit such that v=ab ==> 1=ab(v^-1) ==> 1=a[b(v^1)] ==> a is unit. So according to this, v is irreducible. Am I right? Help!!!! Thanks.