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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Arnautov V. I., Mikhalev A. V., “Topologicheskii analog teoremy Gilberta o bazise”, Tiraspolskii simpozium po obschei topologii i ee prilozheniyam, Kishinev, 1979, 6–7 | MR

[2] Burbaki N., Obschaya topologiya. Osnovnye struktury, Nauka, M., 1969 | MR

[3] Burbaki N., Obschaya topologiya. Topologicheskie gruppy, chisla i svyazannye s nimi gruppy i prostranstva, Nauka, M., 1969 | MR

[4] Feis K., Algebra: koltsa, moduli i kategorii, 1, Mir, M., 1977