This information sheet indicates how the course will be organized at pandemic code level yellow and green.
If the colour codes change during the academic year to orange or red, modifications are possible, for example to the teaching and evaluation methods.

Rings and modules

Course Code :1600WETRMO
Study domain:Mathematics
Academic year:2020-2021
Semester:1st semester
Sequentiality:Min 8/20 for Groups and rings and Lineair algebra and Geometry OR enrolled for Educational master science and techology
Contact hours:60
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:Dutch
Exam period:exam in the 1st semester
Lecturer(s)Wendy Lowen

3. Course contents *

Chapter 1 - Rings and ideals: we develop the basic theory of (not necessarily commutative) rings. Topics: posets and Zorn's Lemma, rings and ideals, quotients, prime and maximal ideals, Noetherian rings, the Chinese remainder theorem.

Chapter 2: UFD: we develop the classical theory of unique factorisation domains, principal ideal domains and euclidean domains.

Chapter 3 - Modules: basic notions, projective and injective modules, tensor product and flat modules, finitely generated modules, exact rows and diagram chasing, modules over principal ideal domains.

Chapter 4 - Commutative rings: we develop the theory in close connection with the elements of algebraic geometry. Topics include: the spectrum, Hilbert's Nulstellensatz, local rings.