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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 569NON-COMMUTATIVE RINGS3 + 02nd Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective The aim of this lesson is to learn the theorems of non commutative rings.
Course Content The Jacobson Radical , Modules, Radical of Ring, Artinian Rings, Semi-Simple Artinian Rings, Semi-Simple Rings, Density Theorem, Applications of Wedderburn Theorem, Commutative Theorems, Wedderburn Theorem and Some Generalizations, Some Special Rings, Simple Algebras, Brauer Group, Maximal Subfields, Some Classic Theorems, Cross Product, Properties of Finite Groups, Hurwitz Theorem and Applications to Group Theory, Polynomial Identities, Kaplansky Theorem, Goldie’s Theorem, Ultra-Products, The Golod- Shafarevitch Theorem.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Learns The Jacobson Radical , Modules, Radical of Ring, Artinian Rings, Semi-Simple Artinian Rings, Semi-Simple Rings.
2Expresses and proves the Density Theorem.
3Learns Applications of Wedderburn Theorem, Commutative Theorems, Wedderburn Theorem and Some Generalizations, Some Special Rings, Simple Algebras.
4Learns Maximal Subfields, Some Classic Theorems, Cross Product, Properties of Finite Groups, Hurwitz Theorem and Applications to Group Theory, Polynomial Identities, Kaplansky Theorem, Goldie’s Theorem, Ultra-Products, The Golod- Shafarevitch Theorem.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0015 54 5  
LO 0024 44    
LO 00355 4    
LO 004 4     4
Sub Total149912 5 4
Contribution42230101

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course






195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2023-2024 Fall1SERPİL HALICI
Details 2021-2022 Spring1SERPİL HALICI
Details 2020-2021 Fall1SERPİL HALICI
Details 2018-2019 Fall1SERPİL HALICI
Details 2014-2015 Fall1SERPİL HALICI
Details 2011-2012 Spring1MUSTAFA AŞCI


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 569 NON-COMMUTATIVE RINGS 3 + 0 1 Turkish 2023-2024 Fall
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. SERPİL HALICI shalici@pau.edu.tr FEN A0316 %70
Goals The aim of this lesson is to learn the theorems of non commutative rings.
Content The Jacobson Radical , Modules, Radical of Ring, Artinian Rings, Semi-Simple Artinian Rings, Semi-Simple Rings, Density Theorem, Applications of Wedderburn Theorem, Commutative Theorems, Wedderburn Theorem and Some Generalizations, Some Special Rings, Simple Algebras, Brauer Group, Maximal Subfields, Some Classic Theorems, Cross Product, Properties of Finite Groups, Hurwitz Theorem and Applications to Group Theory, Polynomial Identities, Kaplansky Theorem, Goldie’s Theorem, Ultra-Products, The Golod- Shafarevitch Theorem.
Topics
WeeksTopics
1 RINGS AND SUBRINGS
2 IDEALS AND QUOTIENT RINGS
3 PRIME AND MAXIMAL IDEALS
4 NILRADİCAL AND JACOBSEN RADICAL
5 MODULES
6 ALGEBRAS
7 RINGS AND MODULES OF FRACTIONS
8 LOCAL PROPERTIES
9 EXAM
10 NOTHERIAN RINGS
11 ARTIN RINGS
12 DEDEKIND DOMAINS
13 EXERCISES
14 EXAM
Materials
Materials are not specified.
Resources
ResourcesResources Language
Türkçe
INTRODUCTION TO COMMUTATIVE ALGEBRA,M. F. ATIYAH, I.G. MACDONALD,1969English
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes