Finitely generated projective module

Summary

A finitely generated projective module over a ring is a direct summand of a free module $R^n$ of finite rank. These modules are the building blocks of $K_0$ of a ring. Over a field they are the finite-dimensional vector spaces, and over a local ring they are the free modules of finite rank. By the Serre–Swan theorem, over a ring of continuous functions they correspond to vector bundles.