SYLLABUS

MODERN ALGEBRA

Four credits

COURSE OBJECTIVES

To study the more deepping properties of algebraic structures, which are introduced in the course of Higher Algebra, especially the finite groups, solvable, nilpotent groups, the finite conditions for rings, the integral domains UFD, PID, Dedekind domains.

PREREQUISITES

- None.

DETAILED COURSE OUTLINE

1. Groups

1.1. Direct product

1.2. Isomorphism theorems

1.3. Center and Commutant

1.4. Sylow’s theorems for finite groups

1.5. Solvable groups

1.6. Nilpotent groups

1.7. Free groups

2. Rings

2.1. Operations over ideals

2.2. Direct product

2.3. Isomorphism theorems

2.4. Finite conditions

3. Integral Domains

3.1. Divisibility in the integral domains

3.2. Principal Ideal Domains (PID)

3.3. Unique Factorization Domains (UFD)

3.4. Dedekind’s Domain

COURSE MATERIALS

1. Joseph J. Rotman, An Introduction to the Theory of Groups, Four Edition, Spriger- Verlag, 1994.

2. S. Lang, Algebra, Addison-Wesley Publishing Company, 1965.