Assume we have a quotient ring $R'=\mathbb{C}[t]/(t-1) $. How can I find the ideals of $ R' $ by using the cannonical homomorphism $ H$ from $\mathbb{C}[t] $ to $ R' $.
This is my homework actually but since I want to deal with it my self I quite modified the question.
This appears to be an application of the Correspondence Theorem. Find the ideals $I$ of $\mathbb{C}[t]$ such that $(t-1) \subseteq I \subseteq \mathbb{C}[t]$. (Hint: there aren't many.) The ideals of $R'$ will be of the form $I/(t-1)$,