When $\mathfrak m^2$ is the unique minimal ideal in a local ring $(R,\mathfrak m)$?
Note that in this case $\mathfrak m^3=0$ in $R$. Furthermore assume that $\operatorname{char}(R)$ is finite.
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Change the title to reflect better the question and some other small improvements
user26857
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Local ring $(R,\mathfrak m)$ such that $\mathfrak m^2$ is the unique minimal ideal
lina
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