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**C**as an algebra over the reals

**R**. The author of the book I have in front of me (Dirac operators in Riemannian Geometry, p.13) writes

[tex]\mathbb{C}\otimes_{\mathbb{R}}\mathbb{C}=\mathbb{C}\oplus\mathbb{C}[/tex]

(as real algebras). Does anyone know what this canonical algebra isomorphism is? Obviously, woz -->(w,z) is not even linear.