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Regular version of the site
2017/2018

Commutative Algebra

Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type: Optional course (faculty)
When: 1, 2 module
Instructors: Christopher Ira Brav, Satoshi Kondo, Vladimir Zhgoon
Language: English
ECTS credits: 5

Course Syllabus

Abstract

This course program sets minimal requirements to the knowledge and skills of students and determines the contents and kinds of lectures and reporting. The program is intended for lecturers teaching this course, course assistants and students of 01.04.01 specialization «Mathematics» who study the course “Infinite Dimensional Lie Algebras and Vertex Operator Algebras”
Learning Objectives

Learning Objectives

  • The course aims at making the students familiar with the basics on commutative ring theory. The students are to learn the basic concepts and notions that may be applicable in algebraic geometry
Expected Learning Outcomes

Expected Learning Outcomes

  • Knows the basic concepts of the commutative ring theory and its connection to algebraic geometry. Is able to understand the fundamental theorems such as Hilbert nullstellensatz and the notion of primary decomposition in Noetherian ring theory.
Course Contents

Course Contents

  • Categories and Direct Limits
  • Rings and Modules
  • Nullstellensatz
  • Primary Decomposition
Assessment Elements

Assessment Elements

  • non-blocking test
  • non-blocking homework
  • non-blocking exam
    the students are required to participate in the problem sessions in order to be able to take the examinations
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.7 * exam + 0.03 * homework + 0.27 * test
Bibliography

Bibliography

Recommended Core Bibliography

  • Altman, A., & Kleiman, S. (2013). A term of Commutative Algebra. United States, North America: Worldwide Center of Mathematics. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.55CA89AB

Recommended Additional Bibliography

  • Dolgachev, I. (2012). Classical Algebraic Geometry : A Modern View. Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=473170