Geodesic
On a problem of Kaplanskii
Izvestiya. Mathematics, Tome 7 (1973) no. 3, pp. 479-496 
Yu. P. Razmyslov. On a problem of Kaplanskii. Izvestiya. Mathematics, Tome 7 (1973) no. 3, pp. 479-496. http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a0/
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     title = {On a~problem of {Kaplanskii}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article we construct for any natural number $n$ an associative multilinear polynomial whose values on matrices of order $n$ are scalar matrices at least one of which is nonzero.

[1] Kaplansky I., “Problems in the theory oi rings”, Nat. Acad. Sci. Nat. Res. Cons., 502 (1957), 1–3 | MR

[2] Latyshev V. N., Shmelkin A. L., “Ob odnoi probleme Kaplanskogo”, Algebra i logika, 8:4 (1969), 447–448 | Zbl

[3] Kaplansky I., “Problems in the theory of rings”, Amer. Math. Mon., 77:5 (1970), 445–454 | DOI | MR | Zbl

[4] Razmyslov Yu. P., “Ob engelevykh algebrakh Li”, Algebra i logika, 10:1 (1971), 33–44 | MR | Zbl