2 citations · 2 across the 4 of their papers we have counts for
7 papers
The Groebner basis and solution set of a polynomial system related to the Jacobian conjecture
Valeria Ramirez, Christian Valqui
We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture, and describe completely the solution set.
Hopf q-braces structures on rank one pointed Hopf algebras
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
In this paper we determine all the Hopf q-brace structures on rank one pointed Hopf algebras and compute the socle of each one of them. We also identify which among them are Hopf s…
Number of homogeneous components of counterexamples to the Dixmier conjecture
Jorge Guccione, Juan Jose Guccione, Christian Valqui
Assume that and are elements of satisfying . The Dixmier Conjecture for says that they always generate . We show that if is a sum of not mor…
On two conjectures about the intersection of longest paths and cycles
Juan Gutiérrez, Christian Valqui
A conjecture attributed to Smith states that every pair of longest cycles in a -connected graph intersect each other in at least vertices. In this paper, we show that every…
The Groebner basis of a polynomial system
Christian Valqui, Marco Solorzano
We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers.
A short and elementary proof of Jung's theorem
Christian Valqui, Jorge A. Guccione, Juan J. Guccione
We give a short and elementary proof of Jung's theorem, which states that for a field K of characteristic zero the automorphisms of K[x,y] are generated by elementary automorphisms…