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On the Existence of the Graded Exponent for Finite Dimensional $\mathbb{Z}_p$-graded Algebras |
Canad. Math. Bull. 55(2012), 271-284
Published:2011-05-30
Printed: Jun 2012
Printed: Jun 2012
- M. Onofrio Di Vincenzo,
- Vincenzo Nardozza,
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 |
| MSC Classifications: |
16R50 - Other kinds of identities (generalized polynomial, rational, involution) 16R10 - $T$-ideals, identities, varieties of rings and algebras 16W50 - Graded rings and modules |