# Continuous module

In mathematics, a **continuous module** is a module *M* such that every submodule of *M* is essential in a direct summand and every submodule of *M* isomorphic to a direct summand is itself a direct summand. The endomorphism ring of a continuous module is a clean ring.[1]

## References

- Camillo, V.P.; Khurana, D.; Lam, T.Y.; Nicholson, W.K.; Zhou, Y. (2006). "Continuous modules are clean".
*Journal of Algebra*.**304**: 94–111. doi:10.1016/j.jalgebra.2006.06.032.

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