"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Special topics of module theory
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MA028
7
2+2+0
6
optional
Matematică
MA028
7
2+2+0
6
optional
Matematică-Informatică
Teaching Staff in Charge
Lect. BREAZ Simion Sorin, Ph.D., bodo@math.ubbcluj.ro
Aims
We shall present basic notions in Module Theory with applications in Abelian Group Theory and in Basic Linear Algebra. The students will solve problems concerning the general theory and they will apply these results to the mentioned particular cases and other.
Content
1. Notions of ring theory.
2. Modules, basic properties.
3. Direct products and direct sums of modules.
4. Free modules.
5. Artinian and noetherian modules.
6. Semisimple modules.
7. Projective modules.
8. Injective modules.
9. Tensor products of modules.
References
1. Anderson, F.W., Fuller, K., Rings and categories of modules, Springer-Verlag, Berlin, 1992.
2. Ion, I.D., Radu, N., Algebra, EDP, Bucuresti, 1990.
3. Nastasescu, C., Inele. Module. Categorii, Ed. Academiei, Bucuresti, 1976.
4. Purdea, I., Tratat de algebra moderna, vol. II, Ed. Academiei, Bucuresti, 1982.
5. Rowen, L.H., Ring theory, vol.I, Academic Press, New York, 1988.
6. Sharpe, D.W., Vamos, P., Injective modules, Cambridge Univ. Press, 1972.
7. Wisbauer, R., Foundations of module and ring theory, Gordon and Breach, Reading, 1991.
Assessment
Exam.