Let $A=k[T_1,T_2]/(T_1 ^2,T_2 ^2,T_1 T_2)$ with k a field and $X=A/rad(A)$. Then in a paper, it says that there is a short exact sequence $0 \rightarrow X \rightarrow A \rightarrow A/(T_1) \rightarrow 0$.
I think $rad(A)=<\overline{T_1}, \overline{T_2}>$, so I can't get this short exact sequence. Who can tell me where I'm wrong? Thank you.