FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 2, PAGES 157-183

**On identities of right alternative metabelian Grassmann algebras**

S. V. Pchelintsev

Abstract

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The right alternative metabelian (solvable of index $2$) Grassmann algebras of
rank $1$
and $2$ are
studied.
A basis of identities of a right alternative metabelian
Grassmann algebra of rank $1$ is presented.
Then it is proved that the variety generated by the indicated algebra
has almost finite topological rank.
It is also shown that the variety generated by a Grassmann
algebra of rank $2$ is not Spechtian.

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Last modified: May 23, 2007