Geodesic
A countable simple quasiregular ring
Matematičeskie zametki, Tome 4 (1968) no. 4, pp. 399-403.

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An example is constructed of a countable simple quasiregular ring. Among others, it follows from our results that the existence of a simple nilring implies the existence of a countable simple nilring. 
@article{MZM_1968_4_4_a2,
     author = {Yu. M. Ryabukhin},
     title = {A countable simple quasiregular ring},
     journal = {Matemati\v{c}eskie zametki},
     pages = {399--403},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_4_a2/}
}
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Yu. M. Ryabukhin. A countable simple quasiregular ring. Matematičeskie zametki, Tome 4 (1968) no. 4, pp. 399-403. http://geodesic.mathdoc.fr/item/MZM_1968_4_4_a2/