×

The standard identity in characteristic \(p\): A conjecture of I. B. Volichenko. (English) Zbl 0795.16017

The main result of this interesting paper is to answer in the affirmative the conjecture of I. B. Volichenko that any PI-algebra over a field of positive characteristic satisfies the standard identity. This means (in contrast to the case of characteristic 0) that in positive characteristic the standard identity cannot be used for the characterization of the \(T\)- ideals of the identities satisfied by a finitely generated algebra. As a consequence of the proof the author establishes the nice result that any PI-algebra over a field of positive characteristic satisfies the same multilinear polynomial identities as some nil-algebra of bounded index.
Reviewer: V.Drensky (Sofia)

MSC:

16R10 \(T\)-ideals, identities, varieties of associative rings and algebras
16R50 Other kinds of identities (generalized polynomial, rational, involution)
16N40 Nil and nilpotent radicals, sets, ideals, associative rings
16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
Full Text: DOI

References:

[1] Kemer, A. R., Identities of the finitely-generated algebras over infinite field, Izvestia Academii Nauk SSSR Seria Mat., 54, 4, 726-753 (1990) · Zbl 0784.16016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.