4 citations · 8 across the 19 of their papers we have counts for
22 papers
Characterization of the centrally finite Amitsur-Small division rings
Elad Paran
In 1978, Amitsur and Small asked whether, for every division ring , maximal left ideals of contract to maximal left ideals in smaller polynomial subrings. Ch…
On Landweber`s unique factorization problem
Adam Jones, Elad Paran
We solve a long-standing open problem, posed by Landweber in 1974: Let be the ring of polynomials in countably many variables over a field . Is the for…
The Combinatorial Nullstellensatz, Chevalley-Warning Theorem and weak Finitesatz in skew polynomial rings
Gil Alon, Angelot Behajaina, Elad Paran
We study zeros of polynomials in the multivariate skew polynomial ring , where is an automorphism of a division ring . We prove a generalization of Nog…
Images of polynomial maps and the Ax-Grothendieck theorem over algebraically closed division rings
Elad Paran, Tran Nam Son
We study the images of polynomial maps over algebraically closed division rings. Our first result generalizes the classical Ax-Grothendieck theorem: We show that if $ f_1, \ldots,…
On a problem of Amitsur and Small
Elad Paran
We construct an example of a division ring and a maximal left ideal in the polynomial ring in two central variables over , such that the intersection $M \cap D[…
On the geometry of zero sets of central quaternionic polynomials II
Gil Alon, Adam Chapman, Elad Paran
Following the work of the first and last authors [2], we further analyze the structure of a zero set of a left ideal in the ring of central polynomials over the quaternion algebra…