NONFINITELY BASED VARIETIES OF RIGHT ALTERNATIVE METABELIAN ALGEBRAS

摘要

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