En matemáticas, particularmente en álgebra abstracta y álgebra homológica, el concepto de módulo proyectivo sobre un anillo R es una generalización más flexible de la idea de un módulo libre (es decir, un módulo con vectores de base). Hay varias caracterizaciones equivalentes de estos módulos.

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In mathematics, particularly in abstract algebra and homological algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizations of these modules appear below. A free module is a projective module, but the converse may be wrong over some rings, such as Dedekind rings. However, every projective module is a free module over a principal ideal domain, and over a polynomial ring over a field or the integers (this is Quillen–Suslin theorem). Projective modules were first introduced in 1956 in the influential book Homological Algebra by Henri Cartan and Samuel Eilenberg.

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