COURSE UNIT TITLE

: COMMUTATIVE RING THEORY I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5055 COMMUTATIVE RING THEORY I ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ENGIN MERMUT

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The aim of this course is to to introduce methods in studying commutative rings and modules over them.

Learning Outcomes of the Course Unit

1   Will be able to understand the motivation for commutative algebra that comes from algebraic geometry, algebraic number theory and invariant theory.
2   Will be able to use the properties of the tensor product of modules over commutative rings and tensor product of algebras.
3   Will be able to use the localization techniques.
4   Will be able to use the properties of the Noetherian and Artinian rings.
5   Will be able to use the properties of discrete valuation rings and Dedekind domains.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Roots of commutative algebra: Algebraic geometry and algebraic number theory, invariant theory.
2 Commutative rings and ideals. Prime and maximal ideals. Nilradical and the Jacobson radical.
3 Modules. Algebras.
4 Tensor product.
5 Modules over principal ideal domains.
6 Canonical forms for square matrices.
7 Rings and modules of fractions. Localization.
8 Primary decomposition.
9 Integral dependence and valuations.
10 Affine algebras over fields.
11 Chain conditions on modules.
12 Noetherian rings. Artinian rings.
13 Discrete valuation rings and Dedekind domains. Fractional ideals.
14 Completions.

Recomended or Required Reading


Textbook(s):
M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison Wesley, 1994.
Supplementary Book(s):
[1] Rodney Y. Sharp, Steps in Commutative Algebra, 2nd edition, Cambridge University Press, 2004.
[2] David Eisenbud, Commutative Algebra: with a View Toward Algebraic Geometry, Springer, 1999.
[3] H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1989.
[4] Irving Kaplansky, Commutative Rings, The University of Chicago Press, 1974.
[5] D. W. Sharpe and P. Vámos, Injective modules, Cambridge University Press, 1972.

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

Homework
1 Midterm Exam
Final Exam

Assessment Criteria

%30 (Homework) + %30 (Midterm examination) +%40 (Final examination)

Language of Instruction

English

Course Policies and Rules

You can be successful in this course by studying from your textbooks and lecture notes on the topics to be covered every week, coming to class by solving the given problems, establishing the concepts by discussing the parts you do not understand with your questions, learning the methods, and actively participating in the course.

Contact Details for the Lecturer(s)

Engin Mermut
e-mail: engin.mermut@deu.edu.tr
Phone: (232) 301 85 82

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 3 42
Preparation for midterm exam 1 15 15
Preparation for final exam 1 20 20
Preparing assignments 10 5 50
Final 1 3 3
Midterm 1 3 3
TOTAL WORKLOAD (hours) 175

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.1433222433
LO.2433222433
LO.3433222433
LO.4433222433
LO.5433222433

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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