Is zero in every ideal? Let $I \subseteq R$ be a subset of a ring $(R, +, \cdot)$ such that


$(I, + )$ is a group
$\forall x \in I, r \in R: xr \in I \text{ and } rx \in I$


Then $I$ is called an "Ideal"

Question: Is 0 in every ideal of any ring?
$(I,+)$ is a subgroup of $(R,+)$. What do you know about the identity of subgroups in relation to the containing group?
the interesting thing is that 0 is always an ideal in any ring.
the second interesting thing is a ring is always ideal for itself 
meaning nothing is ideal for everybody 
and each one is ideal for  itself