One-Sided Ideal Growth of Free Associative Algebras

• Autores: V.M. Petrogradsky
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 149, Nº 3, 2006, págs. 243-249
• Idioma: inglés
• DOI: 10.1007/s00605-005-0374-4
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• Resumen

  • 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.