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 of. 1) a countable family of almost nilpotent varieties of at most linear growth and. 2) an uncountable family of almost nilpotent varieties of at most quadratic growth.

title = "An uncountable family of almost nilpotent varieties of polynomial growth",

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 of. 1) a countable family of almost nilpotent varieties of at most linear growth and. 2) an uncountable family of almost nilpotent varieties of at most quadratic growth.",

author = "Angela Valenti and Sergey Mishchenko",

year = "2018",

language = "English",

volume = "222",

pages = "1758--1764",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier",

}

TY - JOUR

T1 - An uncountable family of almost nilpotent varieties of polynomial growth

AU - Valenti, Angela

AU - Mishchenko, Sergey

PY - 2018

Y1 - 2018

N2 - 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 of. 1) a countable family of almost nilpotent varieties of at most linear growth and. 2) an uncountable family of almost nilpotent varieties of at most quadratic growth.

AB - 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 of. 1) a countable family of almost nilpotent varieties of at most linear growth and. 2) an uncountable family of almost nilpotent varieties of at most quadratic growth.