Introduction to ring theory 1000-1M08WTP
The aim of the course is to give an introduction to the theory of noncommutative rings. Various properties of commutative and noncommuative rings will be compared. The theory will be accompanied by many interesting examples. In particular, the following topics will be presented:
1. Constructions leading to rings and algebras which are important in various applications.
2. Prime and primitive rings.
3. Density Theorem of Jacobson and Chevalley
4. Ring sof quotients and localization:
(a) Theorem of Goldie;
(b) localizations and prima ideale in noetherian rings
5. Noncommutative Nullstellenstz.
Course coordinators
Type of course
Prerequisites (description)
Bibliography
1. K.R.Goodearl, R. B. Warfield, An Introduction to Noncommutative Noetherian Rings.
2. C. Kassel, Quantum Groups.
3. T.Y. Lam, A First Course in Noncommutative Rings.
4. T.Y. Lam, Lectures on Modules and Rings.
5. S. Montgomery, Hopf Algebras and Their Actions on Rings.
6. J.C. McConnell, J.C. Robson, Noncommutative Noetherian Rings.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes: