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matrix ring Noetherian, Artinian, semisimple?
Let $k$ be a field and $\Lambda=\begin{bmatrix}
k & 0 \\
k^2 & k[x]/(x^2)
\end{bmatrix}$. This ring is an algebra over $k$.
(a) What is $\dim_k \Lambda$?
(b) Is $\Lambda$ a left ...
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