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Module Theory, as a book category, collects works that develop and apply the algebraic study of modules — generalizations of vector spaces where scalars come from arbitrary rings rather than fields. Such books range from advanced undergraduate introductions to graduate-level monographs and typically cover basic definitions and examples (submodules, quotient modules, homomorphisms), structural results (finitely generated modules, modules over PIDs, Noetherian/Artinian conditions), and deeper topics used across modern algebra: projective, injective and flat modules, tensor products, homological tools (Ext, Tor, exact sequences), and connections with representation theory, commutative algebra and category theory. Readers can expect a mix of linear algebra intuition and ring-theoretic techniques, with applications to classification problems, algebraic geometry, and module-theoretic approaches to rings.

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