I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2008, VOLUME 14, NUMBER 5, PAGES 171-184
D. I. Piontkovski
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We consider a couple of versions of the classical Kurosh problem
(whether there is an infinite-dimensional algebraic algebra?) for
varieties of linear multioperator algebras over a field.
We show that, given an arbitrary signature, there is a variety of
algebras of this signature such that the free algebra of the variety
contains polylinear elements of arbitrarily large degree, while the
clone of every such element satisfies some nontrivial identity.
If, in addition, the number of binary operations is at
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