# Math 4325 Modern Algebra Homework

## Dr. Duval

For Tuesday, May 3, keep rereading Chapter 17. Read ahead all the irreducibility tests in the section Irreducibility Tests that we've skipped so far. Some of the homework problems due on Thursday, May 5 will rely on these.

For Thursday, May 5, reread the Irreducibility Tests section in Chapter 17. Read ahead in Chapter 20 the first two sections: The Fundamental Theorem of Field Theory and Splitting Fields (though it's not clear how much of this we'll discuss on Thursday).

### Computer exercises

You can find these here.
Ch. 3: 2.
Ch. 4: 1.
Ch. 5: 1.

### Homework

Ch. 1: 14, 22.
Ch. 2: 8, 12, 18, 24, 28.
Ch. 2: [grad students only] 14.

Ch. 3: 2, 4, 10, 12, 18, 26.
Ch. 3: [grad students only] 54.
Ch. 4: 4, 6.

Ch. 4: 8, 10, 16, 24, 54.
Ch. 4: [grad students only] 28.
Ch. 5: 2, 12, 18, 26, 34.
Ch. 5: [grad students only] 24.

Ch. 6: 8, 10, 14, 16, 18 (operation is multiplication), 22, 34.
Ch. 6: [grad students only] 26.
Ch. 8: 4, 14 (do not worry about "general case" for either problem).

Ch. 8: 2, 28, 34.
Ch. 7: 8, 12, 16, 46.
Ch. 7: [grad students only] 40.

Ch. 9: 2, 6, 12, 14, 28, 54 (don't generalize).
Ch. 9: [grad students only] 22.

For these exercises, note the difference between "onto" and "to" ("onto" means the homomorphism is surjective).
Ch. 10: 2, 8, 14, 18, 22, 24, 38, 50.
Ch. 10: [grad students only] 28, 40.

Ch. 12: 8, 12, 18.
Ch. 12: [grad students only] 26.
Ch. 13: 10, 12, 14, 20, 26.

Ch. 14: 4, 8, 10, 20, 22, 28, 46.
Ch. 14: [grad students only] 12, 14.

Ch. 15: 2, 8, 14, 20, 26, 56, 58.
Ch. 15: [grad students only] 22, 42.

Note the unusual due date for the following assignment!
Ch. 16: 10, 12, 18, 20, 22, 38, 42, due Tuesday, May 3.
Ch. 16: [grad students only] 46, due Tuesday, May 3.

No additional problems for graduate students this assignment. Ch. 17: 6, 8, 10 [counts double], 12, 14, 24, due Thursday, May 5.