Suppose that $k$ is algebraically closed. Then why the algebra $A = k[x]/(x^n)$ has finite representation type? please clarify the answer.
2026-04-13 16:18:55.1776097135
why the algebra $A = k[x]/(x^n)$ has finite representation type?
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Hint to the exercise: A module over $A$ is the same as a $k$-vector space $V$ together with a $k$-linear endomorphism $f: V\to A$ such that $f^n=0$. Now apply what you know about normal forms of nilpotent endomorphisms of finite-dimensional vector spaces.