1977
DOI: 10.1007/bf01668594
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Complexity of nonmatrix varieties of associative algebras. I

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Cited by 19 publications
(8 citation statements)
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“…In [11] Kemer characterized the varieties of associative algebras V having polynomial growth. He showed that V has such property if and only if G / ∈ V and UT 2 / ∈ V. The sequences of codimensions of the algebras G and UT 2 are well known (see [12,13]) and, as a consequence of Kemer's result, it follows that there exists no variety of associative algebras with intermediate growth between polynomial and exponential. Also, the two algebras G and UT 2 generate the only two varieties of associative algebras with almost polynomial growth.…”
Section: The Algebra Utmentioning
confidence: 95%
“…In [11] Kemer characterized the varieties of associative algebras V having polynomial growth. He showed that V has such property if and only if G / ∈ V and UT 2 / ∈ V. The sequences of codimensions of the algebras G and UT 2 are well known (see [12,13]) and, as a consequence of Kemer's result, it follows that there exists no variety of associative algebras with intermediate growth between polynomial and exponential. Also, the two algebras G and UT 2 generate the only two varieties of associative algebras with almost polynomial growth.…”
Section: The Algebra Utmentioning
confidence: 95%
“…If M k ∈ V, then also M ∈ V for any ≤ k. Therefore, a variety of associative algebras is called non-matrix if it does not contain M 2 . Non-matrix varieties were introduced by V. Latyshev and were studied before, mainly in the case of characteristic zero [11,16,17,18]. Algebras generated by nilelements and their connection with non-matrix varieties were studied in [3,21,22].…”
Section: Characterization Of Non-matrix Varietiesmentioning
confidence: 99%
“…Explicitly, it is the following Its graded codimension sequence can be obtained by Corollary 3.10. Recall that the codimension sequence for UT 2 (K) is c n (UT 2 (K)) = 2 + 2 n−1 (n − 2) (see [18]). Therefore, one has since the equality p n p = n n−1 p−1 holds.…”
Section: Graded Cocharacter Sequences For Ut N (K)mentioning
confidence: 99%