Pi-algebras satisfying identities of degree

Abraham A. Klein*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A method of classification of Pl-algebras over fields of characteristic 0 is described and applied to algebras satisfying polynomial identities of degree 3. Two algebras satisfying the same identities of degree 3 are considered in the same class. For the degree 3 all the possible classes are obtained. In each case the identities of degree 4 that can be deduced from those of degree 3 have been obtained by means of a computer. These computations have made it possible to obtain—except for three cases—all the identities of higher degrees. It turns out that except for a finite number of cases an algebra satisfying an identity of degree 3 is either nilpotent of order 4, or commutative of order 4, namely the product of 4 elements of the algebra is a symmetric function of its factors.

Original languageEnglish
Pages (from-to)263-277
Number of pages15
JournalTransactions of the American Mathematical Society
StatePublished - 1975


  • Codimension
  • Grassmann algebra
  • Opposite algebra
  • Peirce complement
  • Row-echelon norma form
  • Sylow subgroup
  • T-ideal
  • Universal Pl-algebra


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