Geodesic
Hopf Algebra Dual to a Polynomial Algebra over a Commutative Ring
Matematičeskie zametki, Tome 71 (2002) no. 5, pp. 677-685 
V. L. Kurakin. Hopf Algebra Dual to a Polynomial Algebra over a Commutative Ring. Matematičeskie zametki, Tome 71 (2002) no. 5, pp. 677-685. http://geodesic.mathdoc.fr/item/MZM_2002_71_5_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a polynomial algebra $A=R[X]$ or $R[X,X^{-1}]$ in several variables over a commutative ring $R$ with a Hopf algebra structure $(A,m,e,\Delta,\varepsilon,S)$ the existence of the dual Hopf algebra $(A^\circ,\Delta ^\circ,\varepsilon ^\circ,m^\circ,e^\circ,S^\circ)$ is proved.

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