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

Code	Subject	
MML0004	Algebra 2. (Basic Algebraic Structures)	

Section	Sem.	Hours: C+S+L	Category	Type	
Mathematics	2	2+2+0	fundamental	compulsory	
Mathematics and Computer Science	2	2+2+0	fundamental	compulsory	

Teaching Staff in Charge	Prof. MARCUS Andrei, Ph.D., marcus@math.ubbcluj.ro
Prof. CALUGAREANU Grigore, Ph.D., calu@math.ubbcluj.ro	
Aims	Basic notions and results concerning algebraic structures.	
Content	Chapter I. GROUPS
   1. Groups, homomorphisms, subgroups: basic results and examples.
   2. The symmetric group.
   3. Lattice of subgroups. Generated subgroups.
   4. Cyclic groups, order of an element, dihedral group.
   5. Equivalences induced by a subgroup, Lagrange's theorem.
   6. Normal subgroups. Factor group. Examples.
   7. Isomorphism theorems.
   8. Inner automorphisms, conjugation classes.
   9. Products of groups and subgroups.
   10. Classification of groups of small order.
Chapter II. RINGS AND FIELDS
   1. Rings and fields: basic results and examples.
   2. Homomophisms, subrings, subfields.
   3. Residues mod n. Function rings, matrix rings.
   4. Rings of polynomials.    
Chapter III. MODULES AND ALGEBRAS
   1. Modules over commutative rings. Algebras. 
   2. Homomorphisms, submodules, subalgebras. 

	
Bibliography	1. I. PURDEA, I. POP, Algebra, Editura GIL, Zalau, 2003.
 2. I.D. ION, N. RADU, Algebra (ed.4), Ed. Didactica si Pedagogica, Bucuresti 1991. 
 3. J. ROTMAN, Advanced modern algebra, Prentice Hall, NJ 2002.
 4. G. CALUGAREANU, P. HAMBURG: Exercises in basic ring theory, Kluwer, Dordrecht 1998.
 5. S. CRIVEI:  Basic Abstract Algebra, Casa Cartii de Stiinta, Cluj-Napoca 2002.
 6. A. MARCUS : Algebra [http://math.ubbcluj.ro/~marcus]
 7. J. SZENDREI:  Algebra es szamelmelet, Tankonyvkiado, Budapest 1993.
 8. M. BALINT, G. CZEDLI, A. SZENDREI: Absztrakt algebrai feladatok, Tankonyvkiado, Budapest1988.
 9. G. SCHEJA, U. STORCH: Lehrbuch der Algebra 1,2, B.G. Teubner, Stuttgart  1994
10. M. ARTIN:   Algebra, Birkhauser, Basel  1998.
11. I. PURDEA, C. PELEA, Probleme de algebra, EFES Cluj-Napoca 2005.

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