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Title

Infinite independent systems of identities of alternative commutative algebra over a field of characteristic three

Authors 1

Affiliations

  1. Tiraspol State University, The author's home address: Deleanu str 1, Apartment 60, Kishinev MD-2071, Moldova

Abstract

Let ₃ denote the variety of alternative commutative (Jordan) algebras defined by the identity x³ = 0, and let ₂ be the subvariety of the variety ₃ of solvable algebras of solviability index 2. We present an infinite independent system of identities in the variety ₃ ∩ ₂₂. Therefore we infer that ₃ ∩ ₂₂ contains a continuum of infinite based subvarieties and that there exist algebras with an unsolvable words problem in ₃ ∩ ₂₂. It is worth mentioning that these results were announced in 1999 in works of the international conference "Loops’99" (Prague).

Keywords

ENG
nfinite independent system of identities, alternative commutative algebra, solvable algebra, commutative Moufang loop

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Discussiones Mathematicae - General Algebra and Applications
2004/24/1
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Pages:
5-30
Main language of publication
English
Received
2001-08-27
Accepted
2002-12-08
Published
2004

DOI: 10.7151/dmgaa.1072

Exact and natural sciences