401-3132-00L  Commutative Algebra

SemesterAutumn Semester 2015
LecturersP. D. Nelson
Periodicityyearly recurring course
Language of instructionEnglish


AbstractThis course is meant to provide an introduction to commutative algebra that equips the student to start studying the basics of algebraic geometry.
ObjectiveAbout the course: We shall closely follow the text "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald. Wherever possible, there will be extra focus on exercises that lead towards the basics of Algebraic Geometry. Topics include
* Basics about rings, ideals and modules
* Localisation
* Primary decomposition
* Integral dependence and valuations
* Noetherian rings
* Completions
* Basic dimension theory
LiteratureReferences:
1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969)
2. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995)
Prerequisites / NoticePrerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory).