Introduction To Rings And Fields the complete guide

Introduction To Rings And Fields.

This course will cover the basics of abstract rings and fields, which are an important part of any abstract algebra course sequence. We will spend roughly 4-5 weeks on rings. We will begin with definitions and important examples. We will focus cover prime, maximal ideals, and important classes of rings like integral domains, UFDs and PIDs. We will also prove the Hilbert basis theorem about noetherian rings. The last 3-4 weeks will be devoted to field theory. We will give definitions, basic examples. Then we discuss the extension of fields, adjoining roots, and prove the primitive element theorem. Finally, we will classify finite fields.

INTENDED AUDIENCE: B.Sc and M.Sc students studying mathematics