Let A be a PI-algebra over a field of characteristic zero. Here, we prove that if A is an associative algebra, then the sequence of codimensions cn(A), n = 1, 2, . . . of A is eventually non-decreasing. As a consequence, we get that limn?8 logn(cn(A)/exp(A)n) exists and is an integer or a halfinteger, where exp(A) is the PI-exponent of A. For the non-associative case, we construct a non-associative PI-algebra B whose sequence of codimensions is not eventually non-decreasing. © 2014 London Mathematical Society.
Giambruno, A., Zaicev, M. (2014). Growth of polynomial identities: is the sequence of codimensions eventually non-decreasing?. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 46(4), 771-778 [10.1112/blms/bdu031].
Growth of polynomial identities: is the sequence of codimensions eventually non-decreasing?
GIAMBRUNO, Antonino;
2014-01-01
Abstract
Let A be a PI-algebra over a field of characteristic zero. Here, we prove that if A is an associative algebra, then the sequence of codimensions cn(A), n = 1, 2, . . . of A is eventually non-decreasing. As a consequence, we get that limn?8 logn(cn(A)/exp(A)n) exists and is an integer or a halfinteger, where exp(A) is the PI-exponent of A. For the non-associative case, we construct a non-associative PI-algebra B whose sequence of codimensions is not eventually non-decreasing. © 2014 London Mathematical Society.
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