Title: |
Mathematics 720: Algebra I |
Credits: |
3 credits |
Prerequesites: |
Mathematics 421 / 621 or Departmental approval. |
Required for: |
Mathematics 721 |
Suggested Texts: |
Hungerford. Algebra. Springer-Verlag New York. Rotman. Galois Theory. Springer-Verlag New York. |
Supplemental Texts: |
Galois Theory Harold M. Edwards Clssical Galois Theory with Examples Lisa Gaal Field Theory and its Classical Problems Charles R. Hadlock Lectures in Abstract Algebra I. Basic Concepts Nathan Jacobson Lectures in Abstract Algebra III. Theory of Fields and Galois Theory Nathan Jacobson Basic Notations of Algebra Igor R. Shafarevich Algebra, Volume I. Bartel L. van der Waerden |
Graduate level survaey of algebra: groups, rings, fields, Galois theory, and selected advanced topics.
| Groups, Monoids, subobjects and morphisms |
| Groups acting on Sets |
| Quotient monoids and groups |
| Noether Isomorphism Theorems |
| Sylow Theorems |
| Rings, Rngs, and Ideals |
| Classical Localizations (Rings of Quotients) |
| Factorial Rings (UFD's) |
| Principal Ideal Domains (PID's) |
| Modules |
| Structure Theorem for Finitely Generated Modules over a PID |
| Classical Construction Problems |
| Existance and uniqueness of the algebraic closure |
| Galois Correspondance Theorem |
| Solvability |
| Finite Fields |
This course provides an advanced introduction to the tools and methods of algebra. The objective is to provide the student with a sense of understanding, direction, and appreciation of the results of abstraction of algebraic structure.