• Übungszettel 1
  Corrections: Aufgabe 3.
  Define k[x,y]_n to be the subspace of homogeneous polynomials of degree n including the zero polynomial (but not of all polynomials of degree n).
  Also, (k[x,y]_n,k[x,y]_n+1,x,y) should be denoted by M_n+1 (and not by M_n).
  In der deutsche Fassung sollte in Aufgabe 4 (k,0;0,0) durch (k,0;0,0,0) ersetzt werden.
• Übungszettel 2
• Übungszettel 3
• Übungszettel 4
  English version
• Übungszettel 5 (corrected)
  Correction: Problem 5.4 should read as follows: "If \sum l(V_i) = l(V), then ..."
  And one needs the assumption "\sum V_i = V."
• Übungszettel 6
  Correction: In problem 6.3 (b) replace Q₀ by Q₁.
• Übungszettel 7 (corrected)
  Corrections:
  1. The last line of 7.1 has to be dim H(M) = 2.
  2. In 7.3, line 4, the index of β has to be s (not 3).
  3. In (a) and (b), the condition α_r...α₁ ≠ 0 is missing.
• Übungszettel 8
  Correction: The definitions of LOCAL and MAXIMAL are wrong:
  • A submodule is called "maximal" provided it is a proper submodule und is not properly contained in any proper submodule.
  • A module is called "local" provided it contains a proper submodule which contains all proper submodules.
  A further problem: In 8.4, one has to assume that w contains both arrows and formal inverses of arrows - otherwise the band module cannot be written as a factor module of a local string module.
• Übungszettel 9
  Correction: In 9.4, replace "uniform" by "colocal", replace "(or colocal)" by "(or subdirect irreducible)".
• Übungszettel 10
• Übungszettel 11
  Correction: In problem 11.1 (b) the second line should read: Ig g:V' → v is a module honmomorphism such that pg is surjective, then also g is surjective.
• Übungszettel 12
  Corrections: In 12.3 line 2: replace "g = 0" by "g ≠ 0". In 12.4 line 2: After "R = k+I" one should add "as a k-space" and the condition "with Iⁿ = 0 for some n" should be added - otherwise, there are counterexamples!
• Übungszettel 13

Selected solutions

• Remark to 3.1