Take the 2-minute tour ×  Let $R$ be an integral domain with
identity.  A unit of $R$ is an element $u \in R$ which divides
1.  Does this mean every element in $\mathbb R$ (real numbers)
is a unit since every element divides 1?  e.g.: $3$ is a unit
since $\frac{1}{3} \in \mathbb R$  Also, two elements $a,b$ are
called associates if there is a unit $u$ such that $a = bu$.
Doesn't this also mean every element in $\mathbb R$ is
associated with every other element?  share|improve this
question Almost yes. In any field, all elements but 0 are units
and therefore associated with each other. –  martini Nov 7 '12
at 13:43 add comment  1 Answer  up vote 4 down vote accepted
Being associate is an equivalence relation. In any field, there
are exactly two equivalence classes for this relation: the class
of 0 and the class of 1. The class of 0 contains just 0; the
class of 1 contains everything else.  So, in a field, every two
nonzero elements are associates.  share|improve this answer add
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