---
# System prepended metadata

title: Daily Prep 9A -- MTH 350-01
tags: [mth350, ' dailyprep']

---

---
tags: mth350, dailyprep
---

# Daily Prep 9A -- MTH 350-01

## Overview 

Module 9 is the second week of a long look at the basics of rings. In Module 8 we defined the concept of a ring, established some significant examples, and proved a few foundational results. We especially focused on the concept of a *unit* in a ring (an element that has a multiplicative inverse). In Module 9A we are focusing on a concept that was related to units earlier in the course, namely the concept of a **zero divisor**. As in $\mathbb{Z}_n$, a zero divisor is a nonzero element $x$ of a ring such that there is another nonzero element $y$ with $xy = 0$ where "$0$" means the zero element of the ring. 

## Learning objectives 

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. 

- State the definition of a **zero divisor** in a ring. 
- Identify zero divisors in the "famous" rings (or state that there are none).

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. 

- Give line-by-line explanations for proofs of Theorem 7.19, Theorem 7.20, and Theorem 7.21. 
- State the definition of **integral domain**. 
- Identify which of the "famous" rings are integral domains. 
- Identify whether a new ring, or one defined by an abstract pair of operation tables, is an integral domain or not. 
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## Resources for learning

**Reading:** Read through Investigation 7, starting at the definision of *zero divisor* and continuing up to the beginning f the section "Fields and Integral Domains". 

## Exercises 

The exercises for this Daily Prep are found on the Google Form: 

https://docs.google.com/forms/d/e/1FAIpQLSeZohJbcSF3D88062mklDgVMjpthiKZt0eipmyMKdFeUzb68A/viewform


## Submission and grading 

To submit your work, simply submit the Google Form. You will receive a receipt via email to confirm your submission. (Look in your spam folders if you do not see the receipt.) 

A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.