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math.RA2025
Noether's normalization in skew polynomial rings
Elad Paran, Thieu N. Vo
We study Noether's normalization lemma for finitely generated algebras over a division algebra. In its classical form, the lemma states that if is a proper ideal of the ring $R…
math.RA2025
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,…
math.RA2025
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…