MA 661 - Modern Algebra II (Spring 2004)

Course by Uwe Nagel at the University of Kentucky.

Overview

Schedule

MWF, 11:00 - 11:50, CB 343

Material

The second part of the course will be mainly motivated by the study of roots of polynomials. Geometric interpretations will be stressed. The problem of constructing regular n-gons will be solved.
A good part of the course will consist in deriving applications of Galois theory by a deeper study of groups.

CONTENTS:

17. Normal and separable field extensions

18. Characterizations of Galois extensions

19. Group actions

20. Cyclotomic extensions

21. Solvability by radicals

22. Composition series, solvable and simple groups

23. The general polynomial

24. Affine varieties

25. Modules

26. Noetherian rings and modules

27. Hilbert's Nullstellensatz

Homework

Set 11 (pdf-file)
Set 12 (pdf-file)
Set 13 (pdf-file)
Set 14 (pdf-file)
Set 15 (pdf-file)
Set 16 (pdf-file)
Set 17 (pdf-file)
Set 18 (pdf-file)
Set 19 (pdf-file)
Set 20 (pdf-file)
Set 21 (pdf-file)

Literature

D. S. Dummit, R. M. Foote, Abstract algebra (2nd edition).

M. Artin, Algebra.

T. H. Hungerford, Algebra.

S. Lang, Algebra.

Previous Algebra Prelims

Jan 2004 (pdf-file)
June 2003 (pdf-file)
Jan 2003 (pdf-file)

Last Up-date: April 12, 2004