TU Kaiserslautern • Department of Mathematics • Summer Term 2017

«Cohen-Macaulay and Gorenstein Rings»

Prof. Dr. Mathias Schulze

Lecture

Tue./Thu. 8:15-9:45am
room 48-438

Prerequisites

Commutative Algebra

Topics

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

Literature

• W. Bruns, J. Herzog: Cohen-Macaulay Rings, 2nd ed., Cambridge Studies in Adv. Math. 39, 2008, I.1-3 w/o 1.5, 3.6
• A. Altman, S. Kleiman: Introduction to Grothendieck duality theory, Springer LNM 146, 1970, II.1. Completion.
• H. Mastumura: Commutative Ring Theory, Cambridge Studies in Adv. Math. 8, 1986.