A Course in Ring Theory

Abstract

This book is a rigorous and conceptually oriented introduction to ring theory. The emphasis is on structural understanding rather than encyclopedic coverage: rings are studied through ideals, homomorphisms, quotients, and universal properties, with systematic attention to factorization and polynomial rings. Core topics include Euclidean domains, principal ideal domains, unique factorization domains, the Chinese Remainder Theorem, and the structure of polynomial rings. The exposition is proof-based and deliberately paced, with review chapters that consolidate core ideas and include selected worked solutions, and with exercises designed to reinforce conceptual insight.