Discussion between parisa and Thomas

@Thomas:may be we say that when Ideal has transitive law

This all depends a bit on whether or not your rings have a multiplicative identity. If you say that $I$ is an ideal in $J$, that makes it sounds like $J$ is a ring. If a ring has a $1$, then $J= R$, so I am guessing that your rings do not have a mutiplicative identity.