Units, Zero Divisors and Homomorphisms
Friday, May 22: review the solutions for the related group homework assignment
Tuesday, May 26: Learn about units and zero divisors for Rings.
Video: Introduction to units and
zero divisors.
Everyone watch this one.
Video: Proving cancellation on the left.
This shows you how to do problem 4.
You can skip it if you don't need help on problem 4.
Video: Units, zero divisors and
cancellation. This explains how to use problems 4 and 5 to answer
problem 6.
Matrix instruction and review
✎Unit and Zero Divisor Assignment
Wednesday, May 27: Learn about ring homomorphims and relearn about one-to-one, onto functions.
Videos lectures:
✎ Homework 3.3 # 5, 12 a, c, d, e, 19:
Note
for 19, you must prove five conditions i. f is a function, ii. f is
one-to-one, iii. f is onto, iv. f preserves addition, v. f preserves
multiplication
Thursday, May 28: study for the quiz. Note: meeting time is at 1:00 not 11:00
The quiz this week has 4 problems:
- One problem is one of the four proofs from the unit-zero divisor
homework (problems 1, 3, 4 and 5)
- One problem is about cancellation (like problem 6 in the
unit-zero divisor homework)
- One problem will have 3 functions, and you will be asked to prove
or disprove that they are homomorphisms (like 3.3#12). Note that
for this problem you are not being asked to check whether they are
functions, 1-1 or onto, only whether they satisfy the homomorphism
properties.
- One will be a problem like 3.3 # 19
Friday, May 29, take the quiz on units, zero divisors and homomorphisms