Commutative Algebra -1 (MATH 546)

2022 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10
Ayesha Asloob Qureshi aqureshi@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture
Interactive,Project based learning
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Computer Science and Engineering - With Bachelor's Degree *
Computer Science and Engineering - With Master's Degree *
Computer Science and Engineering - With Thesis *
Cyber Security - With Bachelor's Degree *
Cyber Security - With Master's Degree *
Cyber Security - With Thesis *
Data Science - With Thesis *
Electronics Engineering and Computer Science - With Bachelor's Degree *
Electronics Engineering and Computer Science - With Master's Degree *
Electronics Engineering and Computer Science - With Thesis *
Electronics Engineering - With Bachelor's Degree *
Electronics Engineering - With Master's Degree *
Electronics Engineering - With Thesis *
Energy Technologies and Management-With Thesis *
Industrial Engineering - With Bachelor's Degree *
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Leaders for Industry Biological Sciences and Bioengineering - Non Thesis *
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Leaders for Industry Electronics Engineering and Computer Science - Non Thesis *
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Manufacturing Engineering - Non Thesis *
Manufacturing Engineering - With Bachelor's Degree *
Manufacturing Engineering - With Master's Degree *
Manufacturing Engineering - With Thesis *
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) *
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) *
Materials Science and Nano Engineering - With Thesis (Pre.Name: Materials Science and Engineering) *
Mathematics - With Bachelor's Degree *
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Molecular Biology, Genetics and Bioengineering (Prev. Name: Biological Sciences and Bioengineering) *
Molecular Biology, Genetics and Bioengineering-(Prev. Name: Biological Sciences and Bioengineering) *
Molecular Biology,Genetics and Bioengineering-With Thesis (Pre.Name:Biological Sciences and Bioeng.) *
Physics - Non Thesis *
Physics - With Bachelor's Degree *
Physics - With Master's Degree *
Physics - With Thesis *

CONTENT

It is an introductory course on commutative algebra, based on the book of M. F. Atiyah and I. G. Macdonald, titled “Introduction to commutative algebra”. This course aims to cover the following topics. 1. Rings and ideals 2. Rings and Modules of fractions 3. Primary decomposition 4. Integral Dependence and valuations 5. Noether Normalization 6. Chain conditions 7. Noetherian and Artinian rings 8. The Nullstellensatz and Spec of a ring 9. Zariski topology on Spec of a ring 10. Graded rings and modules 11. Dimension theory

OBJECTIVE

To understand the basics of commutative ring theory

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 40
Midterm 40
Quiz 20

RECOMENDED or REQUIRED READINGS

Textbook

Introduction to Commutative Algebra by Michael Atiyah and I. G. Macdonald
Monomial ideals by Jürgen Herzog and Takayuki Hibi
Commutative ring theory by Hideyuki Matsumra