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arXiv · 2609.23713

Automorphic Transcendence Degree, Growth, and Skew Normalization

Dinh Van Hoang·Vo Ngoc Thieu·Phan Thanh Toan
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Abstract

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.

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Dinh Van Hoang, Vo Ngoc Thieu, Phan Thanh Toan. 2026-09-20. Automorphic Transcendence Degree, Growth, and Skew Normalization. https://arxiv.org/abs/2609.23713

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