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PreprintCC BY-NC-ND 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{hoang2026automorphic,
  title = {{Automorphic Transcendence Degree, Growth, and Skew Normalization}},
  author = {Dinh Van Hoang and Vo Ngoc Thieu and Phan Thanh Toan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23713},
  eprint = {2609.23713},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23713},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Automorphic Transcendence Degree, Growth, and Skew Normalization
AU  - Dinh Van Hoang
AU  - Vo Ngoc Thieu
AU  - Phan Thanh Toan
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23713
UR  - https://arxiv.org/abs/2609.23713
AB  - 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.
ER  -