Feynman Liang
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Recent content on Feynman LiangHugo -- gohugo.ioen-usSun, 26 Aug 2018 18:21:50 -0700Prime and Maximal Ideals
https://feynmanliang.com/posts/prime-maximal-ideals/
Sun, 26 Aug 2018 18:21:50 -0700https://feynmanliang.com/posts/prime-maximal-ideals/Motivation Consider the natural numbers $\mathbb{N}$ and order them by divisibility: $a \leq b$ whenever $b$ divides $a$. For example if I give you the set of numbers $${6,12,18,24,30}$$ Then the “largest” number in terms of divisibility is $6$.
This ordering may seem strange; did we just reverse the “usual” ordering on natural numbers? Not quite. While for any $a,b \in \mathbb{N}$ at least one of $a \leq b$ or $b \leq a$ is true, if we consider the numbers $7$ and $10$ under divisibility ordering we see that neither $7 \mid 10$ nor $10 \mid 7$.Noetherian modules and a short exact sequence for quotients
https://feynmanliang.com/posts/noetherian-modules-and-ses-for-quotients/
Sun, 29 Jul 2018 15:04:38 -0700https://feynmanliang.com/posts/noetherian-modules-and-ses-for-quotients/Equivalent characterizations of the Noetherian condition are plentiful (see Hilbert’s Basis Theorem for more) and using them interchangably can be a convenient and succinct way to express proofs. In this post, we explore yet another characterization of Noetherian conditions and bring attention to an important short exact sequence related to quotient constructions which helps clarify why this condition should hold.
Claim The claim of interest is the following:
Let $M$ be a module and $M’ \subset M$ a submodule.Hilbert's Basis Theorem
https://feynmanliang.com/posts/hilbert-basis-theorem/
Thu, 05 Jul 2018 16:24:42 -0700https://feynmanliang.com/posts/hilbert-basis-theorem/Ambitious goals seem to pop up whenever I have free time, but I have a poor track record of hitting them. To fill the extra time I have over the summer, I started reading Eisenbud’s Commutative Algebra texbook as a side project. Let’s hope I get far enough to learn something useful.
In this post, I want to write a bit about a result known as Hilbert’s Basis Theorem (HBT).MathJax and Syntax Highlighting on Ghost
https://feynmanliang.com/posts/mathjax-integration/
Sun, 27 Oct 2013 00:29:39 +0100https://feynmanliang.com/posts/mathjax-integration/MathML Support (MathJax) Thanks to Patrick Edelman for the reference!
Adding LaTeX to Ghost is very simple. Open up ghost/content/themes/YOUR_THEME_NAME/default.hbs. Before </body>, insert:
1 2 3 4 5 6 7 {{! Mathjax configuration}} <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config">MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]} }); Now test it out: $\sum \frac{1}{n} = H\_n$ should yield \(\sum \frac{1}{n} = H_n\).
The configuration is not perfect, however. Action items include:Oops, you are offline.
https://feynmanliang.com/offline/
Mon, 01 Jan 0001 00:00:00 +0000https://feynmanliang.com/offline/Please find an internet connection and try again.