Quadratic Forms over Q
In this very short note, our objective is to classify quadratic forms over the field of rational
, the Hasse-Minkowski theorem.
Prerequisite for reading this note is elementary knowledge of the p
A Short Course on Linear Representations of Finite Groups
The primary goal of this note is to introduce a beginner to the finite dimensional representations of finite groups.
Prerequisite for reading this note is basic group theory and linear algebra.
A note on Complex Representations of GL(2,Fq)
This note is a sequel to ``A Short Course on Linear Representations of Finite Groups''. We concentrate on the representations for the groups of invertible 2 by 2 matrices over finite fields.
Prerequisite for reading this note is ``A Short Course on Linear Representations of Finite Groups''.
A Brief Introduction on Local Class Field Theory
We introduce the Local Class Field Theory and use Lubin-Tate extension to prove the ``Existence Theory''.
Prerequisite for reading this note, apart from Galois theory, is merely a standard introduction to the theory of local fields.
Factorization in Commutative Rings
We show that an Euclidean domain
is always a principle ideal domain
and a principle ideal domain
is always a unique factorization domain
. We also provide examples to show that the converse of these statements are not true.
This note is suitable for college students who knows basic ring theory.
一個 Zariski 的定理
介紹證明 Hilbert's Nullstellensatz 所需的 Zariski 的定理. 並介紹 algebraic element 和 integral element 之間的關係以及 vector space 和 module 之間的關係.
基本知識需要知道大學代數中 ring 和 field 的性質.
Problems in Algebraic Number Theory
Introduction to Coding Theory