Cohn P. Introduction to Ring Theory 1999

Textbook in PDF format

A clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.
Front Matter
Introduction
Remarks on Notation and Terminology
Basics
Linear Algebras and Artinian Rings
Noetherian Rings
Ring Constructions
General Rings
Back Matter