Alexey Kuzmin
Moscow Pedagogical State University, Russia
On almost Spechtian varieties of right alternative metabelian algebras.
Abstract: The variety V of algebras is said to have the Specht property (or to be Spechtian) if any subvariety in V is finitely based. The problems connected with the Specht property of varieties of associative, alternative, Lie, Jordan, Maltsev and other algebras were studied hard since the middle of previous century. One of the most important results in this area is the theorem proved by A.R.Kemer in 1985, saying that the variety of all associative algebras over a field of characteristic 0 is Spectian. However, there are infinitely based varieties of associative algebras over a field of characteristic distinct from 0. Also, there are examples of infinitely based varieties of nearly associative algebras over an arbitrary field. The infinitely based variety V is called almost Spechtian if each of proper subvarieties in V is Spechtian. The first example of an almost Spechtian variety was constructed in 2000 by S. V. Pchelintsev in a variety of centre-by-metabelian alternative algebras over a field of characteristic 3. In the talk we will present the theorem on structure of almost Spectian subvarieties in a variety of right alternative metabelian Jordan-nilpotant algebras with the weak central elasticity identity over an arbitrary field of characteristic distinct from 2.