Hungerford - Algebra



Springer GTM 73.

Algebra

"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."

= Introduction =

= Chapter I: Groups =

= Chapter II: The Structure of Groups =

= Chapter III: Rings =

= Chapter IV: Modules =

Section IV.6: Modules over a Principal Ideal Domain

 * 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.)

Section IV.7: Algebras
= Chapter V: Fields and Galois Theory =

= Chapter VI: The Structure of Fields =

= Chapter VII: Linear Algebra =

= Chapter VIII: Commutative Rings and Modules =

= Chapter IX: The Structure of Rings =

= Chapter X: Categories =