On Rings Asymptotically Close to Associative Rings

The subject of this work is an extension of A. R. Kemer's results to a rather broad class of rings close to associative rings, over a field of characteristic 0 (in particular, this class includes the varieties generated by finite-dimensional alternative and Jordan rings). We prove the finite-basedness of systems of identities (the Specht property), the representability of finitely-generated relatively free algebras, and the rationality of their Hilbert series. For this purpose, we extend the Razymslov-Zubrilin theory to Kemer polynomials. For a rather broad class of varieties, we prove Shirshov's theorem on height.