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.,  marcusmath.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

References
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%)
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject