Tag
Modules
8 resources tagged “Modules” across the knowledge library.
8 items
Guide6 Aug 2026Cofree Modules and Essential ExtensionsCofree modules via Hom from the ring, the adjunction producing enough injectives, essential extensions, and the existence and uniqueness of injective hulls.4 min readRead MoreGuide6 Aug 2026Direct Sums, Products and Split SequencesDirect sums and direct products of modules, their universal properties, the splitting lemma and equivalent characterisations of split short exact sequences.4 min readRead MoreGuide6 Aug 2026Free and Projective ModulesFree modules and bases, projective modules and the lifting property, the equivalence with direct summands of free modules, and projective resolutions.4 min readRead MoreGuide6 Aug 2026Injective Modules and DualizationInjective modules, the extension property, Baer's criterion, divisible groups, and the existence of enough injectives.4 min readRead MoreGuide6 Aug 2026Injective Modules over a Principal Ideal DomainInjective modules over a PID characterised by divisibility, the classification of injective abelian groups, and the resulting short injective resolutions.3 min readRead MoreGuide6 Aug 2026Modules and Module HomomorphismsModules over a ring, submodules and quotients, module homomorphisms, exact sequences, the short five lemma and the snake lemma.4 min readRead MoreGuide6 Aug 2026Projective Modules over a Principal Ideal DomainStructure of projective and finitely generated modules over a PID, the structure theorem, torsion and free parts, and the resulting short projective resolutions.4 min readRead MoreGuide6 Aug 2026The Hom Functor and Left ExactnessThe Hom functor in both variables, its covariant and contravariant forms, left exactness, and the precise sense in which it fails to be exact.4 min readRead More