Daily Prep 11A -- MTH 350-01

--- tags: mth350, dailyprep --- # Daily Prep 11A -- MTH 350-01 ## Overview We've spent the last 3-4 weeks studying the concept of a ring, a fundamental algebraic structure that is found throughout mathematics and which formalizes much of the math we learned in high school. In this module we will look a little closer at the *structure* of a ring. In Module 11A we will see that there can be rings that live within larger rings; those are called **subrings**. In this module, we'll formally define this concept, develop a couple of tests to see if a subset of a ring is a subring, and look at some properties that subrings inherit and don't inherit from their parent rings. ## 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 *subring* of a ring. + Use the definition to decide if a specific subset of a specific ring is a subring of that ring; find examples of a subset of a ring that is *not* a subring. + State which axioms of a ring are inherited by its subsets and which ones are not. + State Theorem 9.4 (The *Subring Test*). **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. + Use Theorem 9.4 (the *Subring Test*) to decide if a specific subset of a specific ring is a subring of that ring. + Determine what properties of a subring must be inherited from its parent ring, and give examples where inheritance fails. ## Resources for learning **Reading:** Read through Investigation 9 in the textbook starting with the section "Introduction" and through the statement of Theorem 9.4. Focus mainly on definition and theorem statements. ## Exercises The exercises for this Daily Prep are found on the Google Form: https://docs.google.com/forms/d/e/1FAIpQLScmabz2je7SNUEjyegw41iRNC0OK4fPOxk18efGVvyGzkma3A/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.