[[Ring theory MOC]]
# Cayley's theorem for rings

Every ring is the [[subring]] of some [[endomorphism ring]].
Let $R$ be a ring, and $\Lambda: R \hookrightarrow \End_{\mathbb{Z}}R$ be its action on itself by left multiplication.
Then $\Lambda$ is a [[ring monomorphism]].[^2009] #m/thm/ring 

  [^2009]: 2009\. [[Sources/@aluffiAlgebraChapter02009|Algebra: Chapter 0]], §III.2.4, ¶2.7, p. 135

> [!missing]- Proof
> #missing/proof

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