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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ {\rm PI}$-algebras satisfying identities of degree $ 3$

Author: Abraham A. Klein
Journal: Trans. Amer. Math. Soc. 201 (1975), 263-277
MSC: Primary 16A38
MathSciNet review: 0349741
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Abstract: A method of classification of PI-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.

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Keywords: Universal PI-algebra, $ T$-ideal, codimension, row-echelon normal form, Sylow subgroup, opposite algebra, Grassmann algebra, Peirce complement
Article copyright: © Copyright 1975 American Mathematical Society