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401-3132-00L  Commutative Algebra

SemesterAutumn Semester 2016
LecturersR. Pink
Periodicityyearly recurring course
Language of instructionEnglish



Catalogue data

AbstractThis course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry. The material in this course will be assumed in the lecture course "Algebraic Geometry" in the spring semester 2017.
ObjectiveWe shall cover approximately the material from
--- most of the textbook by Atiyah-MacDonald, or
--- the first half of the textbook by Bosch.
Topics include:
* Basics about rings, ideals and modules
* Localization
* Primary decomposition
* Integral dependence and valuations
* Noetherian rings
* Completions
* Basic dimension theory
LiteraturePrimary Reference:
1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969)
Secondary Reference:
2. "Algebraic Geometry and Commutative Algebra" by S. Bosch (Springer 2013)
Tertiary References:
3. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995)
4. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989)
5. "Commutative Algebra" by N. Bourbaki (Hermann, Masson, Springer)
Prerequisites / NoticePrerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory).

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits10 credits
ExaminersR. Pink
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 30 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
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Courses

NumberTitleHoursLecturers
401-3132-00 VCommutative Algebra4 hrs
Wed13-15HG G 3 »
Thu15-17HG G 3 »
R. Pink
401-3132-00 UCommutative Algebra1 hrs
Mon15-16HG D 1.1 »
15-16ML F 36 »
R. Pink

Groups

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Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Mathematics BachelorCore Courses: Pure MathematicsWInformation
Mathematics Master(also Bachelor) Core Courses: Pure MathematicsWInformation