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Matematicheskie Zametki, 2016, Volume 99, Issue 3, Pages 404–408
DOI: https://doi.org/10.4213/mzm10797 (Mi mzm10797) 		 
On the Primality Property of Central Polynomials of Prime Varieties of Associative Algebras

L. M. Samoilov

Ulyanovsk State University
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DOI: https://doi.org/10.4213/mzm10797
Abstract: 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 central polynomial, prime variety.
Received: 23.05.2015
Revised: 21.10.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 3, Pages 413–416
DOI: https://doi.org/10.1134/S000143461603010X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: L. M. Samoilov, “On the Primality Property of Central Polynomials of Prime Varieties of Associative Algebras”, Mat. Zametki, 99:3 (2016), 404–408; Math. Notes, 99:3 (2016), 413–416
Citation in format AMSBIB
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