Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

Abstract Algebra II: Homological Algebra

Assignments

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

Textbook
Sections

Problems
 

due
 

A-modules Exercises 16.14/ 1, 2. Wednesday, January 16
Bimodules Given two A-modules M, N, show that HomA(M, N) is an EndA(N)-EndA(M)op-bimodule. Wednesday, January 30
Path Algebras 19.7/ 1-4 Wednesday, February 13
Pushout and Pullback 10.6/ 1, 2; Write up the proof for 19.7/ 4 Wednesday, February 27
Snake Lemma Let Q be the quiver °–>° with one arrow α and K a field. Show that kernel and cokernel define left exact and right exact functors
ker:   mod KQ–> mod K,   M –> ker M&alpha
cok:   mod KQ–> mod K,   M –> cok M&alpha
respectively.
Wednesday, March 26

Last modified:  by Markus Schmidmeier