**Title of the course: **Introduction to Ring Theory**
Instructor: **Prof. Ali Nesin

**İstanbul Bilgi Ü.**

Institution:

Institution:

**31 July – 20 August 2017**

Dates:

Dates:

**Some familiarity with abstract algebra**

Prerequisites:

Prerequisites:

**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