Geodesic
Topologies on a~ring of polynomials, and a~topological analogue of the Hilbert basis theorem
Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 417-430

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A topology is constructed on a ring of polynomials that extends the topology on the coefficient ring and the topology on the set of variables. A topological analogue of the Hilbert basis theorem is proved. Bibliography: 4 titles. 
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     author = {V. I. Arnautov and A. V. Mikhalev},
     title = {Topologies on a~ring of polynomials, and a~topological analogue of the {Hilbert} basis theorem},
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V. I. Arnautov; A. V. Mikhalev. Topologies on a~ring of polynomials, and a~topological analogue of the Hilbert basis theorem. Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 417-430. http://geodesic.mathdoc.fr/item/SM_1983_44_4_a0/