Let A = F [x1, x2, . . . , xn] be a ring of polynomials over a field F on the variables x1, x2, . . . , xn. It is well known (see, for example, [11]) that the study of automorphisms of the algebra Aâ€¦ (More)

We determine structure constants for the universal nonassociative enveloping algebra U(M) of the four-dimensional non-Lie Malcev algebra M by constructing a representation of U(M) by differentialâ€¦ (More)

Let C = F [x1, x2, . . . , xn] be the polynomial ring in the variables x1, x2, . . . , xn over a field F , and let AutC be the group of automorphisms of C as an algebra over F . An automorphism Ï„ âˆˆâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2003

It is proved that the well known Nagata automorphism of the polynomial ring in three variables over a field of characteristic zero is wild, that is, it can not be decomposed into a product ofâ€¦ (More)

We compute the orders of free commutative Moufand loops of exponent 3 with n â‰¤ 7 free generators and find embeddings of such loops into a loop of invertible elements of the free commutativeâ€¦ (More)

Small, L. W., Stafford, J.T., Warfleld, Jr., R.B. (1985): Affine algebras of Gelfand-Kirillov dimension one are PI. Math. Proc. Sot. Camb. Philos. Sot. 97, 407-414. Zbl. 561.16005 Stanley, R. (1978):â€¦ (More)

We prove the unique solvability of a mixed boundary value problem for the p -Laplace operator by means of variational methods. Using the obtained results, we construct an iterative procedure forâ€¦ (More)

The purpose of this paper is to show that over an infinite field of odd characteristic, invariants of G 2 and Spin(7), both acting on several copies of octonions, are generated by the same invariantsâ€¦ (More)