[[Ring]]
# Ring extension

A **ring extension** is the [[embedding]] of a ring $R$ in a larger ring $T$, #m/def/ring 
i.e. a [[Ring monomorphism]] $R \hookrightarrow T$ or equivalently $R$ is a [[subring]] of $T$.
We write $T : R$, and $T$ is thence called an **extension ring** of $R$.
An [[Adjunction of a ring]] is a particularly pertinent way of extending rings. 

## Further terminology

- [[Integral element|Integral extension]]
- [[Module-finite R-monoid]]

## See also

- [[Field extension]]

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#state/develop | #lang/en | #SemBr