ALGEBRA III

Teaching Staff in AY1997 : Hiroshi SUZUKI
- Office : NS-S309, Tel.:3292, E-mail:hsuzuki@icu.ac.jp
Term and Schedule : Autumn Term, Mon. + Wed. 4
Class Room : NS-S312
Class Schedule
Refernces
Galois Theory in Algebra III
List of Exercises
- Ex.1, Ex.2, Ex.3, Ex.4, Ex.5,
  Ex.6, Ex.7, Ex.8
1996 Midterm Test
1996 Final Test
1995 Midterm Test
1995 Final Test
1994 Final Test
Classes in AY1997
Index

Class Schedule

Month/Day	Title	Subjects
December 10	Extension of Fields	Algebraic elements, minimal polynomials, construction of fields Extensions, isomorphisms
15	Degrees of Extensions and Constructibility	Theorem of degrees of extensions, unplottable figures
17	Recitation
22	Recitation
January 7	Automorphisms, Invariant Fields and Splitting Fields	Galois groups and the relation between invariant fields and automorphisms
12	Normality and Separability	Normal Extensions and splitting fields, separable elements
14	Recitation
19	Recitation
21	Midterm Test
26	Degrees and Orders	The theorem relating the degrees of the extensions
28	Galois' Theorem	Fundamental theorem of Galois and its proof
February 2	Recitation
4	Recitation
9	Existence of Roots by Taking Radicals	Solbability of groups and the extensions by radicals
16	Solvability of Galois Groups	Solvability of an equation and its Galois group
18	Recitation
23	Recitation
25	Computation of Galois Groups	Discussion of transcendental numbers or review session is another choice

Final will be given during the final week.
Recitation problems are not assigned. Please solve them and present them on the board voluntarily.

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References

(References for Algebra including groups, rings, fields and modules

Hiroshi Nagao, "Daisugaku", Asakura Publisher (in Japanese)
Very well written and widely used but a bit difficult for individual study. This is the text book used in Algebra I and II, but in Algebra III, we use this book only as a reference book, as our treatment is a bit different.
Serge Lang "Undergraduate Algebra" second edition, Springer-Verlag
Widely used text book. Lang writes a lot of popular text books.
Serge Lang "Algebra" third edition, Addison-Wesley Graduate student's level text book. The material is widely covered but it is possible to read. I, Suzuki, read this as students seminar with friends from sophomore to senior when I was a student.
van der Waerden "Modern Algebra", Springer
Classical text book.
Artin, Emil, "Galois theory", University of Notre Dame Press,1955.(ICU-lib: Class.No : 412/A8085G2M)

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Galois Theory

Golois Theory has its origin in investigating the solution of an algebraic equation. In modern algebra, it is understood as a problem of field extensions. We study a beautiful theory called Galois Theory connecting this collection of intermediate filds of a field extention with the collection of subgroups of the automorphism groups. I hope every one can enjoy Algebra III.

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Go to Index