| Area of Mathematics: | Algebra and Geometry (EAG) | ||
| Semester: | 5ο | ||
| Course ID: | 52201 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | |||
| Instructors: | Giorgos Kapetanakis |
Description
- Principal ideal domains and unique factorization domains.
- Modules (sums, homomorphisms, quotient modules, free modules).
- Modules over principal ideal domains.
- Structure theorem for finitely generated modules over a principal ideal domain
- Applications: Classification of finitely generated abelian groups, matrix canonical forms (rational canonical form, Jordan canonical form)
Bibliography
- M. Atiyah, I. McDonald. Introduction to Commutative Algebra. Addison-Welsey, 1969.
- R. Sharp. Steps in Commutative Algebra. Cambridge University Press, 2000.
