Rings and modules

Course Code :1600WETRMO
Study domain:Mathematics
Academic year:2019-2020
Semester:1st semester
Contact hours:60
Credits:6
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, localisation (commutative).

Chapter 2 - Modules: basic notions, projective and injective modules, tensor product and flat modules, finitely generated modules, exact rows and diagram chasing.

Chapter 3 - Commutative rings: we develop the theory in close connection with the elements of algebraic geometry. Topics include: the spectrum, Hilbert's Nulstellensatz, local rings, dimension.