The proof I am reading is this one here. I don't understand the following:
"Any $d$ in $D$ defines an endomorphism of $d$ by left multiplication".
What endomorphism is defined, and how?
Understanding Frobenius' Theorem on real division algebras
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1 Answers
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The endomorphism is $D\rightarrow D$, $x\mapsto dx$. The word "endomorphism" here means "endomorphism of a real vector space" not "endomorphism of a ring": left multiplication obviously is not a ring homomorphism.