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I assume it's an ideal that generates the whole Ring.

Also is $(x+y)^2$ a non cyclic ideal of $R=\mathbb{C}[x,y]/(x^2,xy,y^2)$.

The notes I'm using don't give a definition of a cyclic ideal, assume it's the same as definition of cyclic group but with group replaced with ring.

Found the definition, now. An ideal M is cyclic if $M=\{rm: r \in R \}$ for $m \in M$.

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