Geodesic
On the Primality Property of Central Polynomials of Prime Varieties of Associative Algebras
Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 404-408

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In the paper, it is proved that, if $f(x_1,\dots,x_n)g(y_1,\dots,y_m)$ is a multilinear central polynomial for a verbally prime $T$-ideal $\Gamma$ over a field of arbitrary characteristic, then both polynomials $f(x_1,\dots,x_n)$ and $g(y_1,\dots,y_m)$ are central for $\Gamma$.
Keywords: associative algebra, multilinear central polynomial, verbally prime $T$-ideal, prime variety.
Mots-clés : prime central polynomial 
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     author = {L. M. Samoilov},
     title = {On the {Primality} {Property} of {Central} {Polynomials} of {Prime} {Varieties} of {Associative} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {404--408},
     publisher = {mathdoc},
     volume = {99},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a9/}
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L. M. Samoilov. On the Primality Property of Central Polynomials of Prime Varieties of Associative Algebras. Matematičeskie zametki, Tome 99 (2016) no. 3, pp. 404-408. http://geodesic.mathdoc.fr/item/MZM_2016_99_3_a9/