I have some question (see below) concerning an argument (red question mark) in following example from Bosch's "Algebraic Geometry and Commutative Algebra". Here the excerpt:
We consider the ring identification $A = K[t_1,t_2]/(t_2^2-t_1^3) \cong \{\sum_{i \in \mathbb{N}}c_i t^i; c_1 =0\}$ and it's maximal ideal $m=(\bar{t_1},\bar{t_2})= (t^2,t^3) \subset A$.
I don't understand why $t^2$ defines a system of parameters of the local (localized by $m$) ring $A_m$? Here the expression "system of parameters" refers to the property introduced in Prop. 2.4.18: The system of parameters is the minimal set generating $m$ in $A_m$. That's not clear to me how to see that $m$ in $A_m$ is generated by the single element $t^2$.