
automorphism mappings
Let R be ring, I ideal of R
Let f is automorphism of R.
let say: (f(x)+4 )f(y)=0, $\displaystyle \forall$ x,y $\displaystyle \in $ I
if i say $\displaystyle {f}^{1 }$ (f(x)+4 ) y = 0, $\displaystyle \forall$ x,y $\displaystyle \in $
whether the statement was valid?
if yes, any reason to explain that? (i know f is invertible cause f is 11, but whether there is a more specific explanation?)

i don't see anything wrong with that.
since $\displaystyle f^{1} $ is also an automorphism, you can even say that (x + $\displaystyle f^{1}$(4))y = 0 for all x,y in I.