An uncountable family of almost nilpotent varieties of polynomial growth |
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Authors: | S.P. Mishchenko A. Valenti |
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Affiliation: | 1. Department of Applied Mathematics, Ulyanovsk State University, Ulyanovsk 432970, Russia;2. Dipartimento di Energia, Ingegneria dell''Informazione e Modelli Matematici, Università di Palermo, 90128 Palermo, Italy |
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Abstract: | A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we present infinite families of such varieties. More precisely we shall prove the existence of1) a countable family of almost nilpotent varieties of at most linear growth and2) an uncountable family of almost nilpotent varieties of at most quadratic growth. |
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Keywords: | Primary 17A50 16R10 16P90 secondary 20C30 |
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