algebra, equivalence relation regarding associates If f(x) ~ g(x) if and only if f and g are associates,
prove this is an equivalence relation
have tried to prove this both ways, struggling

Well you need to show 3 things :


*

*Reflexivity : Take $u=1$

*Symmetry : If $u$ works in one direction, then $u^{-1}$ works in the other.

*Transitivity : If $f(x) = ug(x)$ and $g(x) = vh(x)$, then $f(x) = (uv)h(x)$, and $uv$ is a unit if $u$ and $v$ are.

