## Abstract

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 language | English |
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Pages (from-to) | 263-277 |

Number of pages | 15 |

Journal | Transactions of the American Mathematical Society |

Volume | 201 |

DOIs | |

State | Published - 1975 |

## Keywords

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