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In the book that I read it says that A. Malcev gave such an example in 1936. But I can't find it... any help will be appriciated.

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Searching for "cannot be embedded in a division ring" with Malcev's name yielded this article, which cites the example on the final page.

Malcev, A. L. "On the immersion of an algebraic ring into a field." Mathematische Annalen 113.1 (1937): 686-691.

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    $\begingroup$ Malcev’s paper is freely available here. $\endgroup$ – Brian M. Scott Aug 4 '16 at 15:56

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