Commutative Algebra -1 (MATH 546)

2022 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Ayesha Asloob Qureshi -aqureshi@sabanciuniv.edu,
English
Doctoral, Master
--
Formal lecture
Interactive,Project based learning
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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
Exam 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