Springer GTM 73.
"This book is intended to serve as a basic text for an algebra course at the beginning graduate level. Its writing was begun several years ago when I was unable to find a one-volume text which I considered suitable for such a course."
Chapter I: Groups Edit
Chapter II: The Structure of Groups Edit
Chapter III: Rings Edit
Chapter IV: Modules Edit
Section IV.1: Modules, Homomorphisms, and Exact Sequences Edit
Section IV.2: Free Modules and Vector Spaces Edit
Section IV.3: Projective and Injective Modules Edit
Section IV.4: Hom and Duality Edit
Section IV.5: Tensor Products Edit
Section IV.6: Modules over a Principal Ideal Domain Edit
- Proof of Theorem 6.1: If $ c \neq 0 $, then the R-module epimorphism $ R \mapsto Rc $ of Theorem 1.5(i) is actually an isomorphism. Since R is an integral domain, the kernel of this map is zero, so the map is injective. Consequently, any ideal I of a PID R is isomorphic, as an R-module, to R. (The potentially frightening implications in the finite case are dismissed by recalling that finite integral domains are already fields.)