Are units considered irreducible

moont14263 · Dec 15, 2011

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.

zhentil · Dec 18, 2011

Huh? Is the question about which word was being defined in the definition?

mathwonk · Dec 18, 2011

no. units are not irreducibles by definition.

Are units considered irreducible

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