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math.RA2004★ 6 cited
Automorphisms fixing a variable of K<x,y,z>
Vesselin Drensky, Jie-Tai Yu
We study automorphisms of the free associative algebra K<x,y,z> over a field K which fix z and such that the images of x, y are linear with respect to x, y. We prove that some of t…
math.AG2004
Test polynomials, retracts, and the Jacobian conjecture
Vladimir Shpilrain, Jie-Tai Yu
Let K[x,y] be the algebra of two-variable polynomials over a field K. A polynomial p=p(x, y) is called a test polynomial (for automorphisms) if, whenever ϕ(p)=p for a mapping ϕof K…