Special topics of module theory |
ter |
|||||
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. |