arXiv subjects

Dinh Van Hoang

Publications and source records attributed to Dinh Van Hoang.

2 recordsLinked to original sources

arXiv2026

Automorphic Transcendence Degree, Growth, and Skew Normalization

We study automorphic transcendence degree for quotients of multivariate skew polynomial rings over a division ring D. We identify this invariant with relative growth dimension, the degree of the relative Hilbert polynomial, and a coordinate dimension determined by leading monomials. We establish invariance under finite module extensions, integral extensions, and investigate the Gelfand-Kirillov dimension under a local finiteness condition. When the coefficient automorphisms are independent modulo inner automorphisms, we prove that a quotient is automorphically normalizable precisely when its automorphic transcendence degree equals the number of nonnilpotent coordinate variables, and classify all such normalization subrings.

math.RA↗

arXiv2026

Noether's normalization in iterated skew polynomial rings

The classical Noether Normalization Lemma states that if $S$ is a finitely generated algebra over a field $k$, then there exist elements $x_1,\dots,x_n$ which are algebraically independent over $k$ such that $S$ is a finite module over $k[x_1,\dots,x_n]$. This lemma has been studied intensively in different flavors. In 2024, Elad Paran and Thieu N. Vo successfully generalized this lemma for the case when $S$ is a quotient ring of the skew polynomial ring $D[x_1,\dots,x_n;σ_1,\dots,σ_n]$. In this paper, we investigate this lemma in a more general setting when $S$ is a quotient ring of an iterated skew polynomial ring $D[x_1;σ_1,δ_1]\dots[x_n;σ_n,δ_n]$. We extend several key results of Elad Paran and Thieu N. Vo to this broader context and introduce a new version of Combinatorial Nullstellensatz over division rings.

math.RA↗