自同构超越度、增长与斜正规化

中文摘要 AI 辅助

我们研究了除环D上多元斜多项式环的商环的自同构超越度。我们将该不变量与相对增长维数、相对希尔伯特多项式的次数以及由首项单项式确定的坐标维数等同起来。我们建立了在有限模扩张和整扩张下的不变性，并在局部有限条件下研究了Gelfand-Kirillov维数。当系数自同构在模内自同构意义下独立时，我们证明一个商环是自同构可正规化的，当且仅当其自同构超越度等于非幂零坐标变量的个数，并对所有这样的正规化子环进行了分类。

英文摘要

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.

发表机构

• Faculty of Advanced Education, Ho Chi Minh City University of Technology and Engineering（胡志明市工程技术大学高级教育学院）
• Department of Computer Science, University of Bath（巴斯大学计算机系）
• Analytical and Algebraic Methods in Optimization Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University（顿铎成大学数学与统计学院优化分析代数方法研究组）

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