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School of Science
Department of Mathematics
|Level of Studies||
|Independent Teaching Activities||
Lectures (Weekly Teaching Hours: 3, Credits: 6)
|Language of Instruction and Examinations||
|Is the Course Offered to Erasmus Students||
|Course Website (URL)||See eCourse, the Learning Management System maintained by the University of Ioannina.|
The principal aim of the course is to introduce the students to the main tools and methods of the theory of non-commutative rings, where by non-commutative ring is meant an associative ring with unit, which is not necessarily commutative.
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.
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
Classroom (face to face)
|Use of Information and Communications Technology||
|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.
- Nathan Jacobson: "Basic Algebra I & II", W. H. Freeman and Company, (1985 & 1989).
- I.N. Herstein: "Non-commutative 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).