6 citations · 6 across the 2 of their papers we have counts for
5 papers
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…
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…
Affine varieties with equivalent cylinders
Vladimir Shpilrain, Jie-Tai Yu
A well-known cancellation problem asks when, for two algebraic varieties , the isomorphism of the cylinders and $V_2 \times {\bf…
Peak reduction technique in commutative algebra
Vladimir Shpilrain, Jie-Tai Yu
The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduce…
Embeddings of curves in the plane
Vladimir Shpilrain, Jie-Tai Yu
In this paper, we contribute toward a classification of two-variable polynomials by classifying (up to an automorphism of ) polynomials whose Newton polygon is either a triang…