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Are units considered irreducible

  1. Dec 15, 2011 #1
    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.
     
  2. jcsd
  3. Dec 18, 2011 #2
    Huh? Is the question about which word was being defined in the definition?
     
  4. Dec 18, 2011 #3

    mathwonk

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    no. units are not irreducibles by definition.
     
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