Resumen de One-Sided Ideal Growth of Free Associative Algebras

V.M. Petrogradsky

• Let R be a finitely generated associative algebra with unity over a finite field . Denote by a n (R) the number of left ideals J ? R such that dim R/J = n for all n = 1. We explicitly compute and find asymptotics of the left ideal growth for the free associative algebra A d of rank d with unity over , where d = 1. This function yields a bound a n (R) = a n (A d ), , where R is an arbitrary algebra generated by d elements. Denote by m n (R) the number of maximal left ideals J ? R such that dim R/J = n, for n = 1. Let d = 2, we prove that m n (A d ) ¿ a n (A d ) as n ? 8.