Title of the course: Introduction to Ring Theory
Instructor: Prof. Ali Nesin
Institution: İstanbul Bilgi Ü.
Dates: 31 July – 20 August 2017
Prerequisites: Some familiarity with abstract algebra
Level: Math majors and graduate students
Abstract: Definition and basic properties. Examples: polynomial rings, power series, group rings,
endomorphisms of an abelian group. Invertible elements, nilpotent elements. Subrings and generators.
Direct sums and direct products. Idempotents. Ideals, ideal generated by a subset and quotient rings.
Homomorphisms of rings. Fundamental theorem of ring theory and its applications. Commutative rings.
Primes and irreducibles. Principal ideal domains. More on polynomial rings.
Language: Depending on the audience English or Turkish