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In this paper, we study the element-wise factorization properties of $D$. For example, we determine when an irreducible element of $D_n$ is an irreducible element of $D$, in terms of $n$ and $p$. 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In this paper, we study the element-wise factorization properties of $D$. For example, we determine when an irreducible element of $D_n$ is an irreducible element of $D$, in terms of $n$ and $p$. In particular, we show that if $F$ is algebraically closed or a "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"If F is algebraically closed or a finite field of char(F)=p, then D has no irreducible element. 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