Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

Module Theory

Homework assignments

All problem numbers refer to our textbook by Claus Michael Ringel and Jan Schröer, Representation Theory of Algebras I: Modules.

Textbook
Sections

Problems
 

due
 

Part I, J-modules.
Section 2
2.10/ 1, 2, 4 Friday, 9/2
Lattice of submodules only problem 2 in 2.10 Friday, 9/9
Examples of submodules problems 2.10/ 5, 6, part of 4: V=N(2,1) Friday, 9/16
Examples of homomorphisms Problems 3.9/ 2, 3, 4 Friday, 9/23
Direct sums and summands Show Lemma 3.6 (ii), Problems 3.9/ 5, 6 Friday, 9/30
Short exact sequences Problems 3.9/ 7 ("only if" part), 9, 10 Friday, 10/7
K[T]-modules Exercise in 5.2, First 2 exercises in 5.4 Friday, 10/14
...intermission...
time to prepare presentations or the term paper, or to grade... until Friday, 10/21
Simple modules Problems 6.3/ 2, 4, 5 Friday, 10/28
Cyclic modules Problems 7.4/ 1, 2, 3 Friday, 11/4
Finite length modules Problems 8.3/ 1, 2, 3 Friday, 11/11
Local rings Problems 10.4/ 2, 3 Monday, 11/21

Last modified:  by Markus Schmidmeier