A Six Generalized Squares Theorem, with Applications to Polynomial Identity Algebras Academic Article uri icon


  • The theories of superalgebras and of P.I. algebras lead to a natural Z 2-graded extension of the integers. For these generalized integers, a "six generalized squares" theorem is proved, which can be considered as a Z 2-graded analogue of the classical "four squares" theorem for the natural numbers. This theorem was conjectured by A. Berele and A. Regev ("Exponential Growth of Some P.I. Algebras," [BR2]) and has applications to p.i. algebras. © 2001 Academic Press.

author list (cited authors)

  • Cohen, P. B., & Regev, A.

citation count

  • 5

publication date

  • May 2001