ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

Discussiones Mathematicae - General Algebra and Applications

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Discussiones Mathematicae - General Algebra and Applications


Discussiones Mathematicae General Algebra and Applications 24(1) (2004) 5-30


Nicolae Ion Sandu

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



Let \frak A3 denote the variety of alternative commutative (Jordan) algebras defined by the identity x3 = 0, and let \frak S2 be the subvariety of the variety \frak A3 of solvable algebras of solviability index 2. We present an infinite independent system of identities in the variety \frak A3 Ç\frak S2\frak S2. Therefore we infer that \frak A3Ç\frak S2\frak S2 contains a continuum of infinite based subvarieties and that there exist algebras with an unsolvable words problem in \frak A3 Ç\frak S2 \frak S2.

It is worth mentioning that these results were announced in 1999 in works of the international conference ``Loops'99'' (Prague).

Keywords: infinite independent system of identities, alternative commutative algebra, solvable algebra, commutative Moufang loop.

2000 Mathematics Subject Classification: 17D05, 20N05.


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Received 27 August 2001
Revised 8 December 2002
Revised 16 June 2004
Revised 14 July 2004