Table of Contents:

• Description
• Homework

• Description

  517 Abstract Algebra II
  4 Hours.
  Prerequisite: Math 516 or equivalent, or permission of the instructor.
  Text: Paolo Aluffi, Algebra: Chapter 0, American Mathematical Society

  This is the second basic graduate algebra course.
  The courses are designed to cover the basic topics in algebra which would be needed
  for a student who intends to pursue research not only in algebra but in various other areas.
  For example, elements of commutative algebra which are needed for algebraic geometry
  are covered in this second course.

  The topics to be covered are:
  Fields: Algebraic extensions, Galois theory, Transcendental Extensions
                 Chapters VII

  Commutatve and Homological Algebra: Hilbert's Nullstellensatz, Primary Decompositions, Integral Extensions
                Chapters VII- IX

  Grading Policy: Homework (30%), Midterm Exam (20%) and Final (50%).
   
   

  Homework

  HOMEWORK 1. Due Wednesday 1/22/14:

  p. 397: 1.5, 1.6,1.7, 1.8. 1.11, 1.12, 1.13. 1.14, 1.15, 1.18, 1.24, 127. 1.27, 1.28, 1.29

  p. 414: 2.2, 2.3, 2.16

  HOMEWORK 2. Due Wednesday 1/29/14

  p. 438: 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.10, 4.11, 4.12

  HOMEWORK 3, Due 2/7/14

  p. 452: 5.3, 5.4, 5.8, 5.9, 5.14, 5.15, 5.18, 5.21, 5.23

  p. 466: 6.1, 6.3, 6.4, 6.5, 6.6

  HOMEWORK 4, Due 2/14/14

  p. 466: 6.7, 5.8, 6.9, 6.11, 6.15, 6.16, 6.17, 6.18, 6.19

  p.480: 7.3, 7.4, 7.6, 7.8, 7.9, 7.10, 7.11, 7.12, 7.13

  Take Home Exam Due 3/1/14

  HOMEWORK 5. Due 2/28/14

  P. 480: 7.14, 7.15, 7.16, 7.19

  HOMEWORK 6. Due 3/14/14

  P, 496: 1.2, 1.4, 1.5, 1.6, 1,.7, 1.9, 1.10, 1.11, 1.17,1.18, 1.19, 1.20, 1.21, 1.25

  p.511: 2.2, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9

  HOMEWORK 7. Due 4/4/14

  P. 511: 2.16, 2.17, 2.19, 2.20, 2.21, 2.22, 2.23, 2.24, 2.25

  p.520: 3,3, 3.6, 3.10, 3.14, 3.15

  p.532: 4.4, 4.6, 4.7, 4.9, 4.11, 4.12

  HOMEWORK 8, Due 4/11/14

  P.532: 4.18, 4.19, 4.20, 4.22

  p.543: 5.1, 5.2, 5.3, 5.4, 5.9, 5.12, 5.15, 5.17

  p.555: 6.1, 6.4, 6.5, 5.5, 6.9, 6.10, 6.11, 6.12, 6.13, 6.14,

  6.18, 6.21, 6.22

  HOMEWORK 9. Due 4/18/14

  P.574 : 1.4, 1.7, 1.13,1.14, 1.15, 1.17

  p.589: 2.4, 2.14, 2.15, 2.17

  p.602: 3,3, 3.4, 3.7, 3.11, 3.14, 3.15

  HOMEWORK 10. Due 4/25/14

  p.614: 4.1, 4.3, 4.6, 4.10, 4.11, 4.12, 4.13, 4.14

  p.626: 5.1, 5.2, 5.5, 5.6, 5.8,5.9,5.10, 5.11, 5.12, 5.13, 5.14

  HOMEWORK 12. Due 5/2/14

  p. 658: 7.5, 7.6, 7.7, 7.9, 7.11, 7.12,7.13, 7.14, 7.15, 7.16, 7.18