Geodesic
On the completeness of topological rings in maximal topologies
Sbornik. Mathematics, Tome 187 (1996) no. 2, pp. 159-174

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The article studies rings that are direct sums of an infinite family of subrings. The question of the completeness of these rings in maximal ring topologies is investigated for various classes of ring topologies. In particular it is shown that if the continuum hypothesis is assumed, then both complete and non-complete maximal ring topologies exist on a ring that is an infinite direct sum of copies of the same finite field. 
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     author = {V. I. Arnautov},
     title = {On the completeness of topological rings in maximal topologies},
     journal = {Sbornik. Mathematics},
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     volume = {187},
     number = {2},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_2_a0/}
}
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V. I. Arnautov. On the completeness of topological rings in maximal topologies. Sbornik. Mathematics, Tome 187 (1996) no. 2, pp. 159-174. http://geodesic.mathdoc.fr/item/SM_1996_187_2_a0/