Ring isomorphism is an equivalence relation Is there an elementary proof showing that a ring isomorphism is an equivalence relation? Isomorphism is defined as usually is, a bijective homomorphism $\phi$. any help is appreciated.

A relation $R$ is an equivalence relation if it is:


*

*reflexive, i.e. $xRx$ for all $x$

*symmetric, i.e. if $xRy$ then $yRx$

*transitive, i.e. if $xRy$ and $yRz$ then $xRz$


You need to prove all three properties.
