Alexey Kuz'min
USP, Brazil
On basic superranks of some varieties of algebras.
August 22, 2012
Abstract: Let V be a variety of algebras, A be an algebra in V and var(A) be the variety generated by A. A basic rank of variety V is a minimal number of generators of A such that var(A)=V.
Consider the following varieties of algebras over a field of characteristic 0:

• the variety generated by associative Grassmann algebra;
• the variety of alternative metabelian algebras;
• the variety of Jordan metabelian algebras;
• the variety of Malcev metabelian algebras.

It is not hard to show that the basic rank of each variety from this list is infinite.
For a variety V of infinite basic rank one can consider a more delicate tool that is called basic superrank of variety V.
We provide the definition of basic superrank and calculate its values for the varieties from the given list.