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${\mathbf Z}_n$-graded polynomial identities
of the full matrix algebra of order $n$


Author: Sergei Yu. Vasilovsky
Journal: Proc. Amer. Math. Soc. 127 (1999), 3517-3524
MSC (1991): Primary 16R40
DOI: https://doi.org/10.1090/S0002-9939-99-04986-2
Published electronically: May 13, 1999
MathSciNet review: 1616581
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Abstract | References | Similar Articles | Additional Information

Abstract: The algebra $M_n(F)$ of all $n\times n$ matrices over a field $F$ has a natural $\mathbf{Z}_n$-grading $M_n(F)=\sum _{\alpha\in \mathbf{Z}_n}\bigoplus\mathcal{M}_n^{(\alpha )}$. In this paper graded identities of the $\mathbf{Z}_n$-graded algebra $M_n(F)$ over a field of characteristic zero are studied. It is shown that all the $\mathbf{Z}_n$-graded polynomial identities of $M_n(F)$ follow from the following:

\begin{displaymath}x_1x_2-x_2x_1=0,~~~~\alpha (x_1)=\alpha (x_2)=\overline{0};\end{displaymath}

\begin{displaymath}x_1xx_2-x_2xx_1=0,~~~~\alpha (x_1)=\alpha (x_2)=-\alpha (x).\end{displaymath}


References [Enhancements On Off] (What's this?)

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Additional Information

Sergei Yu. Vasilovsky
Affiliation: Department of Mathematics, University of Swaziland, Private Bag 4, Kwaluseni, Swaziland, Southern Africa; Institute of Mathematics, Novosibirsk 630090, Russia
Email: vasilovs@realnet.co.sz

DOI: https://doi.org/10.1090/S0002-9939-99-04986-2
Keywords: Graded polynomial identities, full matrix algebra
Received by editor(s): April 10, 1997
Received by editor(s) in revised form: February 26, 1998
Published electronically: May 13, 1999
Communicated by: Ken Goodearl
Article copyright: © Copyright 1999 American Mathematical Society

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