On the variety of algebras of type (-1,1)
The author shows that the variety of (-1,1) algebras, over a field of characteristic 0, is the join of the variety M generated by the free (- 1,1) algebra of rank 2 and the variety N of strongly (-1,1) algebras. The author has shown earlier that the variety M is decomposable [Sib. Mat. Zh. 22, No.3, 162-178 (1981; Zbl 0468.17008)]. He conjectures here that the variety N is generated by an algebra he has constructed in [Izv. Akad. Nauk SSSR, Ser. Mat. 50, No.1, 79-100 (1986; Zbl 0609.17008)]. If so, the free algebra of the variety N is prime, and the variety N would be indecomposable.
scientific article; zbMATH DE number 4002341