I have to prove that the ring is a subring of any ring
Let S= and R= then S is a subring of R iff is a ring and and S is a ring with the same operations.
As we know S has an identity element of 0 --> 0+0=0
It has an additive inverse of 0 --> 0-0=0
Its commutative and associative
and its distributive over addition.
So my only problem is that I am having difficulties cleaning this up and putting it into a proof.
Maybe you can help me