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On the Existence of the Graded Exponent for Finite Dimensional $\mathbb{Z}_p$-graded Algebras

  Published:2011-05-30
 Printed: Jun 2012
  • M. Onofrio Di Vincenzo,
    Dipartimento di Matematica e Informatica, Università degli Studi della Basilicata, Viale dell'Ateneo Lucano 10, 85100 Potenza, Italia
  • Vincenzo Nardozza,
    Dipartimento di Matematica, Università degli Studi di Bari, via Orabona 4, 70125 Bari, Italia
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Abstract

Let $F$ be an algebraically closed field of characteristic zero, and let $A$ be an associative unitary $F$-algebra graded by a group of prime order. We prove that if $A$ is finite dimensional then the graded exponent of $A$ exists and is an integer.
Keywords: exponent, polynomial identities, graded algebras exponent, polynomial identities, graded algebras
MSC Classifications: 16R50, 16R10, 16W50 show english descriptions Other kinds of identities (generalized polynomial, rational, involution)
$T$-ideals, identities, varieties of rings and algebras
Graded rings and modules
16R50 - Other kinds of identities (generalized polynomial, rational, involution)
16R10 - $T$-ideals, identities, varieties of rings and algebras
16W50 - Graded rings and modules
 

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