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If $e$ is a positive integer, $F_*^e(R)$ denotes the $R$-algebra structure induced on $R$ via the $e$-times iterated Frobenius map ( $r\\rightarrow r^{p^e}$ ). We show an existence of a matrix factorization of $f$ whose cokernel is isomorphic to $F_*^e(R)$ as $R$-module. 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