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Answer to Question #17118 in Abstract Algebra for sanches

Question #17118
Let R be an n2-dimensional algebra over a field k. Show that R ∼ Mn(k) (as k-algebras) iff R is simple and has an element r whose minimal polynomial over k has the form (x − a1) • • • (x − an) where a1, . . . , an ∈ k.
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