AA:D&F

Solutions to exercises from Abstract Algebra by Dummit & Foote. (Not all links are active.)

Chapter 0: Preliminaries
Chapter 1: Introduction to Groups
Chapter 2: Subgroups
Chapter 3: Quotient Groups and Homomorphisms
Chapter 4: Group Actions
Chapter 5: Direct and Semidirect Products and Abelian Groups
Chapter 6: Further Topics in Group Theory
Chapter 7: Introduction to Rings
Chapter 8: Euclidean Domains, Principal Ideal Domains, and Unique Factorization Domains
Chapter 9: Polynomial Rings
Chapter 10: Introduction to Module Theory
Chapter 11: Vector Spaces
Chapter 12: Modules over Principal Ideal Domains
Chapter 13: Field Theory
Chapter 14: Galois Theory
Chapter 15: Commutative Rings and Algebraic Geometry
Chapter 16: Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
Chapter 17: Introduction to Homological Algebra and Group Cohomology
Chapter 18: Representation Theory and Character Theory
Chapter 19: Examples and Applications of Character Theory
Appendix I: Cartesian Products and Zorn’s Lemma
Appendix II: Category Theory

Solutions

• Daniel  On October 8, 2010 at 12:06 am

Best Wishes

• lyayanadayana  On September 14, 2011 at 11:31 pm

hello¡¡¡¡

I would like you to help me understand these exercises thanks.

questions

- If a ring has zero divisors I can enlarge to a field F

- If two entire domains D1 and D2 are isomorphic, fields of quotients
are also isomorphic.

- If fi is an isomorphism of fields F1 F2 —– yu units belonging to F1 then the image of u belongs to the units of F2

• lyayanadayana  On September 14, 2011 at 11:34 pm

If fi is an isomorphism of fields F1—— F2 and u belongs units to F1 then the image of u belongs to the units of F2

• julius  On November 7, 2011 at 2:15 pm

Simply Put. You are an awesome man/woman!

• Khaled Qaraman  On November 24, 2011 at 6:01 am

Thanks a lot :) It is really a great work :)

My Regards and Best Wishes :)

• petermarshall555  On December 4, 2011 at 9:17 pm

Peter

• nbloomf  On December 5, 2011 at 10:28 am

Thanks! I’m glad you find it useful.

• petermarshall555  On December 4, 2011 at 9:17 pm

Looking forward to some posts on Homology!

Peter

• Mike  On January 31, 2012 at 2:51 am

I love you… really, I do. Haha, no, but this “crazy project” is an amazing feat and it’s been extremely helpful. Thanks.

• franky  On April 12, 2012 at 3:15 pm

Hi, the links for Sec.12.3 is missing. Could you please fix that so I can learn from it.
Thanks a lot

• franky  On April 12, 2012 at 7:56 pm

Hi,
the link for sec12.3 is missing. I can not find any solutions. could you please put them on there.
Thanks

• JUAN  On May 14, 2012 at 3:53 pm

MUY UTIL

• Mathew  On July 31, 2012 at 5:04 pm

Excellent Excellent Excellent work!

• nbloomf  On July 31, 2012 at 6:29 pm

Thanks!

• Mathew  On July 31, 2012 at 5:08 pm