I need your help on how to show the existence of a bialgebra pairing: for the polynomial ring $k[x]$ over a field $k$, there is a bialgebra pairing $t:k[x]\otimes k[x]→k$ such that $t(x,x)=1$. What is the unique bialgebra pairing satisfying $t(x,x)=1$?
Bialgebra pairing on ring polynomial $K[x]$
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