A backup of a deleted PSQ : https://math.stackexchange.com/q/3955443/290189

OP : irfanmat

It has a detailed answer by Atticus Stonestrom. It’s pity that his post got deleted. As there’s no reason for undeletion, I’m posting it here so as to preserve the contents.

Question body

Is there a semi-simple and projective but not injective module? I will be glad if you help.

Response(s)

In the non-commutative case, the answer is yes. Consider $R$ the ring of upper triangular $2\times 2$ matrices over a field $F$, and denote by $e_{ij}$ the element of $R$ with the $ij$-th entry equal to $1$ and all other entries equal to $0$. We can decompose $R$ as a direct sum of left ideals $$Re_{11}\oplus (Re_{12}+Re_{22})=Re_{11}\oplus Re_{22},$$ so let $M=Re_{11}$. Then $M$ is clearly simple, and – as a direct summand of the free module $R$ – is also projective. However, $M$ is not injective; consider the map $f:Re_{11}\oplus Re_{12}\to M$ taking $e_{11}$ and $e_{12}$ to $e_{11}$. $Re_{11}\oplus Re_{12}$ is a left ideal of $R$, but there is no way to extend $f$ to a map $R\rightarrow M$, so this gives the desired example.

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I wanted to post the following answer to a question on double integral on Math.SE, but someone had submitted his work before I finished typing. As a result, I’m posting this on my personal blog.

Let $r = \sqrt{x^2+4y^2}$ and $t = \begin{cases} \tan^{-1}(2y/x) &\text{ if } x > 0 \\ \pi/2 &\text{ if } x = 0. \end{cases}$ Then $\begin{cases} x &= r \cos t \\ y &= (r \sin t)/2 \end{cases}$ and $D = { (r,t) \mid r \ge 0, t \in [\pi/4, \pi/2] }$. Calculate the Jacobian

I wanted to start a meta question, but I don’t see a point of that after viewing some related posts listed at the end of the next subsection.

Intended question

You may vote on your preferred way.

Related questions:

My notes for a YouTube video about procrastination on one hearing only.

Why?

1. Boring tasks.

   It’s necessary?

   • Yes: Make it fun.
     • Get a study partner.
     • Find a more energetic time.
   • No: Get rid of it.

2. Surrounding environment.

   • Identify someone who procrastinates in your circle of influence.
   • Distance yourself from them, or
   • Be aware of what their behavior.

3. Perfectionism

   • Know about yourself.
   • Reality: nothing can be perfect.

Five strategies against procrastination:

1. Decompose a huge task into smaller parts.

   [Read More]

Problem

After upgrading to Ubuntu 20.04 form 18.04, I wasn’t able to start GIMP 2.10. The message was in the same format as that in a related Ask Ubuntu question, except that the version numbers were greater.

I attempted installing the package gegl, which was irrelavant to the problem.

Analysis

I found the answers mentioning the package libgegl helpful.

$ dpkg -l | grep gegl
ii  gegl                                       0.4.22-3                         
     amd64        Generic Graphics Library Test Program
ii  libgegl-0.4-0:amd64                        1:0.4.18+om-0ubu18.04.18~ppa     
     amd64        Generic Graphics Library
ii  libgegl-common                             1:0.4.18+om-0ubu18.04.18~ppa     
     all          Generic Graphics Library - common files

Despite deletion of ppa:otto-kesselgulasch/gimp by ppa-purge, that leaves a trace in /etc/apt/sources.list.d.

Just a little linklog to a relevant page on How to Forge. Root privileges are needed.

1. Stop service: service mysql stop

2. Start MySQL server w/o password: mysqld_safe --skip-grant-tables &

3. Connect to CLI client as root: mysql -u root

4. Reset root password. Here’s the syntax for ≥v.5.7.6.

   mysql> use mysql;
   mysql> SET PASSWORD FOR 'root'@'localhost' = PASSWORD("newpass");
   mysql> flush privileges;
   mysql> quit
   

5. Repeat step 1, or killall mysqld if it doesn’t work. Output can be different on different Linux distro.

   [Read More]

Goal

To provide an open-source alternative to the Docker image escalope/pandoc-mermaid-plantuml, whose Dockerfile isn’t available.

The rationale behind these difficult setup is simple: construct informative Mermaid diagram with intuitive Markdown syntax in an open-source and economic way.

This newly constructed Docker image is entirely on GitLab. No Docker Hub account is needed. For sample usage, consult .gitlab-ci.yml in my test project.

Difficulties

1. issues raghur/mermaid-filter#51 and #52
2. issue gitlab-org/gitlab-runner#4566

Useful code/articles

1. time-machine-project/requests-for-comments@470b0c5 Dockerfile
2. Reduce Docker Image Sizes Using Alpine
3. Best practices for building docker images with GitLab CI with the accompanying gist
4. The code block in the highlighted comment in item 2 of the above section
5. pandoc installation for Docker
6. Sample Dockerfile for Alpine Linux in the troubleshooting of Puppeteer
7. sc250024/docker-mermaid-cli@3c9ddb5 src/puppeteerConfigFile.json
8. raghur/mermaid-filter project README’s section about Puppeteer config file

Background

I lacked motivation to keep this tweaked theme up with Hugo’s development after last summer. When I came back yesterday, I saw that some pages using Font Awesome icons were broken. Apart from that, the ToC list level problem resurfaced.

Fixed ToC

The solution that I had adopted no longer worked. Luckily, some users provided a shorter code in the later discussions. The one from user501254 caught me. I first tried to copy his code into the partial layout for ToC. However, nothing changed.

GitHub Actions provide CI/CD support, which might interest many GitHub users. I’ve applied for this feature a week ago. Luckily, my application for the trial was approved by GitHub. Tonight, I’ve found the motivation for making my first step in my forked repo VincentTam/beautiful-jekyll.

My setup:

1. Clicked on the “Action” tab of the repo.
2. Chose the workflow file template for Jekyll.
3. Added a slash / in front of srv in chmod 777 srv/jekyll, so as to fix the “no such file or directory” error.
4. Added the parameter repository: {your repo name} in the site config file _config.yml.

The action should be successfully configured.

Background

I prefer including the date into the Permalink of a post. Everytime I create a new post, I type

hugo new post/$(date -I)-post-title.md

to ensure that the date is correct.

Problem

The title field in the post’s front matter contained the date, which wasn’t something that I wanted because it’s already shown next to the icon.

Observations

Neither \d nor [\d] works for the PCRE character class \d.