Math 3330
Section 5.1
Page 1 of 8
Math 3330
Section 5.1
Rings
* Definition of a Ring *
Let R be a nonempty set on which at least one equivalence relation = and two
operations are defined. Call the operations addition + and multiplication *. Then R is
a ri
Math 3330
Homework 7
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Show your work. If a problem requires a proof, explain and justify your steps carefully.
Homework papers should be legible and neat, and the pages should be stapled together
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Math 3330
Homework 1
Due: September 1, 2016
Name:
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Show your work. If a problem requires a proof, explain and justify your steps carefully.
Homework papers should be legible and neat, and the pages should be stapled together
in the correct o
Math 3330
Homework 4
Due: September 22, 2016
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Show your work. If a problem requires a proof, explain and justify your steps carefully.
Homework papers should be legible and neat, and the pages should be stapled together
in the correct
Math 3330
Homework 6
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Show your work. If a problem requires a proof, explain and justify your steps carefully.
Homework papers should be legible and neat, and the pages should be stapled together
in the correct order. Illegible work ma
Math 3330
Homework 3
Due: September 15, 2016
Name:
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Show your work. If a problem requires a proof, explain and justify your steps carefully.
Homework papers should be legible and neat, and the pages should be stapled together
in the correct
Math 3330
Homework 8
Name:
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Show your work. If a problem requires a proof, explain and justify your steps carefully.
Homework papers should be legible and neat, and the pages should be stapled together
in the correct order. Illegible work ma
Math 3330
Homework 2
Due: September 8, 2016
Name:
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Show your work. If a problem requires a proof, explain and justify your steps carefully.
Homework papers should be legible and neat, and the pages should be stapled together
in the correct o
UH - Math 3330 - Dr. Heier - Spring 2014
HW 8
Due 04/03, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (1 point) Section 3.5, Problem 9
2. (1 point) Section 3.5, Problem 18
3. (1 poi
UH - Math 3330 - Dr. Heier - Spring 2014
HW 10
Due 04/17, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (1 point) Section 4.5, Problem 2
2. (1 point) Section 4.5, Problem 4
3. (1 poi
UH - Math 3330 - Dr. Heier - Spring 2014
HW 6
Due 03/06, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (1 point) Section 3.1, Problem 13
2. (1 point) Section 3.1, Problem 14
3. (1 po
Math 3330
Section 5.2
Math 3330
Section 5.2
Integral Domains and Fields
* Definition: Integral Domain *
Let D be a ring. Then D is called an integral domain if
1. D is commutative
2. D has a unity e that is not 0
3. D has no zero divisors
Example:
n
when
Math 3330
Section 4.6
Page 1 of 8
Math 3330
Section 4.6
Quotient Groups
Start with what we have done in the last two days
1. Products of Subsets
Let A and B be nonempty subsets of the group G. Define the product of AB to be the
subset
AB = cfw_x G| x = ab
Math 3330
Section 5.3
The Quotient Field of an Integral Domain
Motivation:
Consider Integers only elements with multiplicative inverses are 1 and -1.
Create fractions rational numbers to be able to divide. But, division is just the inverse of
multiplicati
Math 3330
Section 6.1
Math 3330
Section 6.1
Ideals and Quotient Rings
* Definition Ideal of a Ring*
The subset I of a ring R is called an ideal if it satisfies the following conditions:
1. I is a subring of R
2. For every r R and for every a I , ar I and
Math 3330
Chapter 8
Page 1 of 9
Math 3330
Chapter 8
Polynomials
You all know what a polynomial is, but lets look at polynomials from an abstract algebra
perspective, and discover some of their most important properties.
Before we visit the familiar polyno
UH - Math 3330 - Dr. Heier - Spring 2014
HW 4
Due 02/20, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (1 point) Section 2.4, Problem 3 (d) and (e)
2. (1 point) Section 2.4, Problem
UH - Math 3330 - Dr. Heier - Spring 2014
HW 9
Due 04/10, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (1 point) Section 4.1, Problem 15
2. (1 point) Section 4.2, Problem 1
3. (1 poi
UH - Math 3330 - Dr. Heier - Spring 2014
HW 5
Due 02/27, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (1 point) Section 2.5, Problem 16
2. (1 point) Section 2.5, Problem 17
3. (1 po
Math 3330
Homework 1
Name:
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Show your work. If a problem requires a proof, explain and justify your steps carefully.
Homework papers should be legible and neat, and the pages should be stapled together
in the correct order. Illegible work ma
Math 3330
Homework 1 Solutions
Name:
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Homework papers should be legible and neat, and the pages should be stapled together
in the correct order. Illegib
Math 3330
Homework 4
Name:
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Homework papers should be legible and neat, and the pages should be stapled together
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Exam 1 Review
Outline of Topics Covered
0 Sets
1 Binary Operations
2 Definition of a Group
3 Fundamental Theorems about Groups
4 Powers of an Element; Cyclic Groups
5 Subgroups
1
Exam 1 Review
Potential Exam Questions
Non-proof problems
set and binary op
UH - Math 3330 - Dr. Heier - Spring 2014
HW 1
Due 01/23, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (1 point) Section 1.1, pages 9/10: True or False (No proofs necessary, just say