Catchup 8

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Nathan Nguyen
2024-10-07 11:20:46 -05:00
parent b54e075ddd
commit bddcc244e5
2 changed files with 2 additions and 2 deletions

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@@ -98,4 +98,4 @@ As a direct consequence, we see the following.
1. Given a field $F$, since $F$ is a PID, it is also a UFD. Thus, $F[x]$ is a UFD.
2. The ring of polynomials over integers, $\mathbb{Z}[x]$ is a UFD.
3. Given $D$ is a UFD, $D[x]$ is a UFD. Thus, $D[x_1, x_2]$ is a UFD, and by induction, $D[x_1, \ldots, \x_n]$ is a UFD.
3. Given $D$ is a UFD, $D[x]$ is a UFD. Thus, $D[x_1, x_2]$ is a UFD, and by induction, $D[x_1, \ldots, x_n]$ is a UFD.