## ANT misprint

Dear Prof Kim,

I was wondering if you could explain to me why in the proof of Corollary 87 in the notes it says that if

$Z[\alpha]= Span\{g_1,...,g_n\}$

and

$Z[\alpha] = Span\{h_1,...,h_m\},$

then $\alpha^i \beta^j$ belongs to the span of $\{g_ih_j\}$.

Is the second $Z[\alpha]$ supposed to be $Z[\beta] = Span\{h_1,...,h_m\}$ or have I missed something?

Any help would be appreciated.
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You are absolutely right It is a misprint that will be eventually corrected.