---
# System prepended metadata

title: Daily Prep 10B -- MTH 350-01
tags: [mth350, ' dailyprep']

---

---
tags: mth350, dailyprep
---

# Daily Prep 10B -- MTH 350-01

## Overview 

We've learned what it means to find integer multiples and exponents of elements in an arbitrary ring, and seen that rules for exponents that we learn in basic high school algebra actually work the same in any number system. In part B of this module, we'll look at a property of rings called the **characteristic**, that pertains to taking integer multiples of ring elements that produce the zero element of the ring. The characteristic of a ring turns out to be a sort of fingerprint that helps us identify other properties the ring has. 

## 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. 

- (*Review*) Given a specific ring, find positive and negative integer multiples of elements in the ring. 
- State the definition of the **characteristic** of a ring. 


**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. 

- Find the characteristic of a given ring. 
- Prove Theorem 8.12. 

## Resources for learning

**Reading:** Read the parts of Investigation 8 in the textbook starting *after* Preview Activity 8.10 and continuing through the end. 

## Exercises 

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

https://docs.google.com/forms/d/e/1FAIpQLSd2l49bESbN8WvGQjKF6bg0iO3BgjBnxMMR6YZWILSVvNe-Kg/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.