Module Handbook

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Course MAT-41-20-K-7

Cohen-Macaulay and Gorenstein Rings (4V, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
4 V Lecture 9.0 CP 56 h 214 h
(4V) 9.0 CP 56 h 214 h

Basedata

SWS 4V
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
Schulze, Mathias, Prof. Dr. (PROF | DEPT: MAT)
+ further Lecturers of the department Mathematics
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State [NORM] Active

Contents

  • regular sequences, depth, projective dimension,
  • reflexive modules,
  • Fitting ideals,
  • Cohen-Macaulay rings and modules,
  • regular and normal rings,
  • complete intersections,
  • canonical module and Gorenstein rings,
  • local duality,
  • algorithmic aspects.

Literature

  • D. Eisenbud: Commutative Algebra with a View towards Algebraic Geometry,
  • W. Bruns, J. Herzog: Cohen-Macaulay Rings,
  • H. Mastumura: Commutative Ring Theory.

Materials

Further literature will be announced in the lecture.

Requirements for attendance (informal)

Modules:

Courses

Requirements for attendance (formal)

None

References to Course [MAT-41-20-K-7]

Module Name Context
[MAT-41-20-M-7] Cohen-Macaulay and Gorenstein Rings P: Obligatory 4V, 9.0 LP