Directions.
- Review the Learning $\LaTeX{}$ document. If you have trouble finding the command for a math symbol you want to use, try looking in this Short Math Guide for $\LaTeX{}$.
- Get the template for this assignment (or use your own). Here’s how to do it:
- Go to www.overleaf.com, and make sure you are logged in.
- In a new window, go here: www.overleaf.com/read/pwbdnyvhnrjh
- Click on the menu icon in the upper-left and select “Copy Project”.
- When ask for a name, choose something like “Math 210B - WA 01” and click “Copy”.
- When this completes you will be back in your own workspace (instead of mine).
- Use $\LaTeX$ to type up your proof(s) of the proposition(s) listed below. Make sure to use complete sentences and appropriate punctuation. Also, make sure to edit for typos.
- Click on the download pdf button (second one to the right of the “Recompile” button). Save the file somewhere you can easily find it.
- Submit the pdf in Canvas under the corresponding assignment.
- Let me know if you have any questions!
Proposition to Prove.
Proposition. Let $R$ be a commutative ring with $1\neq 0$, and let $N$ be the set of all nilpotent elements of $R$. Then $N$ is an ideal of $R$.
Please prove all parts of the proposition. This includes part of Problem #14 from Section 7.1 (see 210A Homework 11) as well as Problem #29 in Section 7.3 (see 210B Homework 01). But you are welcome to use the Binomial Theorem (see Problem #25 of Section 7.3) without proving it.
