I want a book to cover the following topics in Module Theory:
Modules, Submodules, Quotient modules, Morphisms Exact sequences, three lemma, four lemma, five lemma, Product and Co products, Free modules, Projective modules, Injective modules, Direct sum of Projective modules, Direct product of Injective modules.
Divisible groups, Embedding of a module in an injective module, tensor product of modules, Noetherian and Artinian Modules, Finitely generated modules, Jordan Holder Theorem, Indecomposable modules, Krull Schmidt theorem, Semi simple modules, homomorphic images of semi simple modules.
I want a book that covers these topics. It is not that a single book should contain all of these but it would be better if it is so. The book should be interesting, have some good problems to work on (would be better if it is provided with hints to hard problems).
Comments and suggestions are needed.
I recommend "Basic Algebra" (I and II) by Nathan Jacobson.
Volume I covers all the basic notions (Modules, Submodules, Quotient modules, Morphisms, finitely generated modules). Volume II covers Noetherian and Artinian Modules, Jordan Holder Theorem, Krull Schmidt theorem, injective and projective modules, tensor product of modules, etc.
Volume II contains also chapters on category theory and universal algebra (relevant for notions like Product and Coproduct that you mentioned).
These books are really nice and clear, and contain a lot of other basic material in almost every subdomain of algebra I can think of.