Non-finitely based varieties of right alternative metabelian algebras

الأصل · EN

Since 1976, it is known from the paper by V. P. Belkin that the variety RA₂ of right alternative metabelian (solvable of index 2) algebras over an arbitrary field is not Spechtian (contains non-finitely based subvarieties). In 2005, S. V. Pchelintsev proved that the variety generated by the Grassmann RA₂-algebra of finite rank r over a field F, for char(F)≠2, is Spechtian iff r=1. We construct a non-finitely based variety M generated by the Grassmann V-algebra of rank 2 of certain finitely based subvariety V₂ over a field F, for char(F)≠2,3, such that M can also be generated by the Grassmann envelope of a five-dimensional superalgebra with one-dimensional even part.