On the Boyd–Deninger polynomial x+1/x+y+1/y+1, pt. I - The curve
In this post we study the Boyd-Deninger polynomial P(x,y)=x+1/x+y+1/y+1. In particular, we are interested in the elliptic curve that is defined by it.
2025/12/29
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Boolean ring and algebraic numbers
In this post, we study the Boolean ring and see how it can be used in algebraic number theory.
2025/10/13
阅读更多Artin-Schreier Extensions
We are interested in a special category of field extensions. Let $K$ be a field of characteristic $p \ne 0$, we want to know the structure of an extension of $K$ of degree $p$. It turns out that there lies the an Artin-Schreier polynomial of the form $X^p-X-\alpha$.
2025/5/16
阅读更多Equivalent Conditions of Regular Local Rings of Dimension 1
In this post we collect and prove (as detailed as possible) the equivalent conditions of being a Regular local ring of dimension 1.
2025/5/10
阅读更多The Structure of SL_2(F_3) as a Semidirect Product
In this post we determine $SL_2(\mathbb{F}_3)$ using Sylow theory and linear algebra.
2023/11/11
阅读更多A Separable Extension Is Solvable by Radicals Iff It Is Solvable
We show that a separable extension is solvable by radical iff it is solvable, i.e. it has a Galois closure with solvable Galois group. The proof is done in a general setting.
2023/10/21
阅读更多Picard's Little Theorem and Twice-Punctured Plane
We show that the range of a non-constant entire function's range cannot be a twice-punctured plane.
2023/9/18
阅读更多SL(2,R) As a Topological Space and Topological Group
In this post we show that $SL(2,\mathbb{R})$ can be identified as the inside of a solid torus and see what we can learn from it.
2023/8/12
阅读更多Artin's Theorem of Induced Characters
We give a relatively more detailed proof of Artin's theorem in representation theory of finite groups as well as an example of dihedral group.
2023/7/17
阅读更多Chinese Remainder Theorem in Several Scenarios of Ring Theory
We study the Chinese remainder theorem in various contexts and abstract levels.
2023/5/27
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