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A Six Generalized Squares Theorem, with Applications to Polynomial Identity Algebras

✍ Scribed by Paula B. Cohen; Amitai Regev

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 113 KB
Volume: 239
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8681

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✦ Synopsis

The theories of superalgebras and of P.I. algebras lead to a natural ‫ޚ‬ -graded 2 extension of the integers. For these generalized integers, a ''six generalized squares'' theorem is proved, which can be considered as a ‫ޚ‬ -graded analogue of 2 the classical ''four squares'' theorem for the natural numbers. This theorem was Ž conjectured by A. Berele and A. Regev ''Exponential Growth of Some P.I. w x. Algebras,'' BR2 and has applications to p.i. algebras.

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