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This article is cited in 24 scientific papers (total in 24 papers)
Finitely generated special Jordan and alternative $PI$-algebras
I. P. Shestakov
Abstract:
The author explores the question of whether identities related to special Jordan and alternative $PI$-algebras exist in associative algebras. It is proved that if $A$ is a finitely generated special Jordan (alternative) $PI$-algebra, then the universal associative enveloping algebra $S(A)$ (respectively, the universal algebra $\mathscr R(A)$ for right alternative representations) of algebra $A$ is also a $PI$-algebra. As a corollary it is proved that the upper nilradical of a finitely generated special Jordan or alternative $PI$-algebra over a Noetherian ring is nilpotent. A similar result holds for the Zhevlakov radical of a finitely generated free alternative algebra. In addition, a criterion is obtained for local associator nilpotence of an alternative algebra.
Bibliography: 19 titles.
Received: 18.06.1982
Citation:
I. P. Shestakov, “Finitely generated special Jordan and alternative $PI$-algebras”, Mat. Sb. (N.S.), 122(164):1(9) (1983), 31–40; Math. USSR-Sb., 50:1 (1985), 31–40
Linking options:
https://www.mathnet.ru/eng/sm2271https://doi.org/10.1070/SM1985v050n01ABEH002731 https://www.mathnet.ru/eng/sm/v164/i1/p31
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Abstract page: | 508 | Russian version PDF: | 131 | English version PDF: | 4 | References: | 58 | First page: | 2 |
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