Geodesic
Formal solutions of the Hilbert problem for a ring
Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 221-232.

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The solution of the Hilbert problem is defined as the series which formally satisfies the boundary condition. We find a number of such solutions and give their properties. 
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     author = {I. Kh. Sabitov},
     title = {Formal solutions of the {Hilbert} problem for a ring},
     journal = {Matemati\v{c}eskie zametki},
     pages = {221--232},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a14/}
}
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I. Kh. Sabitov. Formal solutions of the Hilbert problem for a ring. Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 221-232. http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a14/