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This time my struggle is with ring ideals. Book still won't provide examples, so I'm again trying to come up with some of my own. I figured {0,2} might fit the definition as an ideal of ##\mathbb{Z/4Z}## since it is an additive subgroup and ##\forall x \in I, \forall r \in R: x\cdot r, r\cdot x \in I##. But I'm not sure if I'm missing something here or, if I'm correct, how to generalize this result. Biggest problem though has been coming up with polynomial ideals, if someone could provide an explicit example I'd be really grateful.