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Let $R=\mathbb Z/4\mathbb Z$ be a ring and the ideal $2\mathbb Z/4\mathbb Z$ is not flat module since $2\mathbb Z/4\mathbb Z$ is generated by a nilpotent element how to prove it?

Sha Vuklia
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Tema
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You have an embedding $0\rightarrow 2Z/4Z\rightarrow Z/4Z$. A $Z/Z4Z$ bilinear form $b$ defined on $2Z/4X\times 2Z/4Z$ is zero. Since you will $b(2,2)=4b(1,1)$. This implies that the tensor product $2Z/4Z\otimes 2Z/4Z$ is zero.

Tsemo Aristide
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