About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 55. Chapters: Direct sum of modules, Simple module, Endomorphism ring, Injective module, Modular representation theory, Frobenius algebra, Tensor product of modules, Serial module, Structure theorem for finitely generated modules over a principal ideal domain, Morita equivalence, Flat module, Projective module, Glossary of module theory, Beauville-Laszlo theorem, Torsion, Composition series, Eilenberg-Mazur swindle, Artinian module, Krull-Schmidt theorem, Semisimple module, Extension of scalars, Algebra representation, Localization of a module, Supermodule, Bimodule, Indecomposable module, Free module, Finitely-generated module, Principal indecomposable module, Global dimension, Essential extension, Resolution, Pairing, Fitting lemma, Depth, Projective cover, Invariant basis number, Injective hull, Schanuel's lemma, Length of a module, Annihilator, Mitchell's embedding theorem, Pure submodule, Torsionless module, Noetherian module, Socle, Cyclic module, Semiperfect ring, Comodule, Elementary divisors, Artin-Rees lemma, Invariant factor, Top, Radical of a module, Primitive ideal, Stably free module. Excerpt: In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, then any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in (Baer 1940) and are discussed in some detail in the textbook (Lam 1999, 3). Injective modules have been heavily studied, and a variety of additional notions are defined in terms of them: I...
