moont14263
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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.
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.