|Part III, A-modules.
Section 15: Path algebras
|15.7/ 1, 3
|Section 15: Path algebras
||15.7/ 2, 4, 5
||Suppose Q is a quiver with no oriented cycles.
Show that the representations P(i)
introduced in class are all projective,
and specify them for the example quiver shown.
||For the example quiver in the previous problem,
specify the projective covers of the simple modules
S(i) and compute the kernels.
Are the kernels projective modules?
Make a conjecture about the kernels of the projective
covers of the simple modules over a path algebra
of a quiver with no oriented cycles!
|Section 25: Push-out and pull-back
||Exercise on p.150 (Uniqueness of push-out), exercise on p.151 (Universal property of the pull-back)
|Section 25: Induced short exact sequence
||Exercise 25.8/ 2.
||Friday, 4/ 6
|Section 27: Projective resolutions
||Proof of Lemma 27.1 on page 173
||Friday, 4/ 20