Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MML0011	Special Topics in Algebra	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics - in Hungarian	6	2+1+0	speciality	optional	
Mathematics-Computer Science - in Hungarian	6	2+1+0	speciality	optional	

Teaching Staff in Charge	Prof. MARCUS Andrei, Ph.D., marcus@math.ubbcluj.ro	
Aims	Notions and results concerning polynomial arithmetic, algebraic equations, field extensions
and Galois theory. Applications
	
Content	Cap. I. ARITHMETIC IN  INTEGRAL DOMAINS
   1. Divisibility.  Prime and irreducible elements.
   2. Factorial domains.
   3. Principal ideal domains.
   4. Euclidean domains.
   5. Arithmetic in rings of polynomials
Cap. II. FIELD EXTENSIONS AND GALOIS THEORY
   1. Finite extensions 
   2. Algebraic extensions 
   3. Adjoining a root. The splitting field of a polynomial
   4. Finite fields.
   5. Algebraically closed fields. The algebraic closure of a field
   6. Separable extensions 
   7. Normal extensions 
   8. The Galois group of an extension
   9. The fundamental theorem  of  Galois theory
  10. Solvability of algebraic equations by radicals
  11. Geometric constructibility by ruler and compas

Bibliography	1. ROTMAN, J.: Advanced modern algebra, Prentice Hall, NJ 2002.
2. SZENDREI J.:  Algebra és számelmélet, Tankönyvkiadó, Budapest 1993.
3. I.D. ION, N. RADU, Algebra (ed.4), Editura Didactica si Pedagogica, 1990. 
4. M. BALINT, G. CZEDLI, A. SZENDREI: Absztrakt algebrai feladatok, Tankonyvkiado, 
     Budapest  1988.
5. M. ARTIN:   Algebra, Birkhauser, Basel  1998.
6. N. BOURBAKI, Algebre, chap. 1-3, Ed. Hermann, Paris 1970.
7. I. PURDEA, I. POP, Algebra, Editura GIL, Zalau, 2003.
8. A. MARCUS: Algebra [http://math.ubbcluj.ro/~marcus]

Assessment	Homeworks (20%). Exam. (80%)