Ring Theory (MAE725)
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 Department of Mathematics
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General
School 
School of Science 

Academic Unit 
Department of Mathematics 
Level of Studies 
Undergraduate 
Course Code 
MAE725 
Semester 
7 
Course Title 
Ring Theory 
Independent Teaching Activities 
Lectures (Weekly Teaching Hours: 3, Credits: 6) 
Course Type 
Special Background 
Prerequisite Courses   
Language of Instruction and Examinations 
Greek, English 
Is the Course Offered to Erasmus Students 
Yes 
Course Website (URL)  See eCourse, the Learning Management System maintained by the University of Ioannina. 
Learning Outcomes
Learning outcomes 
The principal aim of the course is to introduce the students to the main tools and methods of the theory of noncommutative rings, where by noncommutative ring is meant an associative ring with unit, which is not necessarily commutative.


General Competences 
The course aims to enable the undergraduate student to acquire the ability to analyse and synthesize basic knowledge of the Theory of Rings, which is an important part of modern algebra. The contact of the undergraduate student with the ideas and concepts of the theory of rings, (a) promotes the creative, analytical and deductive thinking and the ability to work independently, (b) improves his critical thinking and his ability to apply abstract knowledge in various field. 
Syllabus
Rings  Homomorphisms  Ideals  Quotient Rings  Modules  Rings arising from various constructions  Algebras  Group algebras  Modules over group algebras  Module homomorphisms  The bicommutator  Simple faithful modules and primitive rings  Artin rings  Simple finite dimensional algebras over algebraically closed fields  Artinian modules  Noetherian rings and modules  Jacobson radical.
Teaching and Learning Methods  Evaluation
Delivery 
Classroom (face to face)  

Use of Information and Communications Technology 
 
Teaching Methods 
 
Student Performance Evaluation 
Combination of: Weekly homework, presentations in the class by the students, written work, and, at the end of the semester, written final exams in Greek (in case of Erasmus students, in English) which includes analysis of theoretical topics and resolving application problems. 
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
 Nathan Jacobson: "Basic Algebra I & II", W. H. Freeman and Company, (1985 & 1989).
 I.N. Herstein: "Noncommutative Rings", AMS, Carus Mathematical Monographs 85, (1971).
 Luis Rowen: "Ring Theory (student edition)", Academic Press, Second Edition, (1991).
 T.Y. Lam: "A First Course in Noncommutative Rings", GTM 131, Springer, (2001).
 P. M. Cohn: "Introduction to Ring Theory", Springer (2000).
 Y. Drozd and V. Kirichenko: "Finite Dimensional Algebras", Springer (1994).