MML0011 | Special Topics in Algebra |
Teaching Staff in Charge |
Assoc.Prof. SZANTO Csaba Lehel, Ph.D., szantomath.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 |