臺灣博碩士論文加值系統

設 Q 是佈於有限体F上的非退化二次型式，其中F的特徵數為奇質數。令O為對應於Q的正交群。本篇文章我們將找出在五維空間下，被O固定所形成的不變子環的生成元，並證明此一不變子環是唯一分解環.

Let $Q$ be a nondegenerate quadratic form over the finite field $\mathbb{F}_{q}$
of odd prime power order $q$ with char$\mathbb{F}_{q}\neq 2$
and Let $O_{n}(\mathbb{F}_{q})$ be the associated orthogonal group.
Let $O_{n}(\mathbb{F}_{q})$ act linearly on the polynomial ring
$\mathbb{F}_{q}[x_{1},\ldots,x_{n}].$ In this thesis we find the invariant subring
$\mathbb{F}_{q}[x_{1},x_{2},x_{3},x_{4},x_{5}]^{O_{5}(\mathbb{F}_{q})}$
with explicit generators. We also prove that this subring is a UFD.

Chapter 1 Introdution
Chapter 2 Construction of the Minimal Polynomial of over F
Chapter 3 Construction of the Invariant Ring

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