## Sign map is a homomorphism on the multiplicative group of reals

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.6 Define $\varphi : \mathbb{R}^\times \rightarrow \{ \pm 1 \}$ by $x \mapsto x / |x|$. Describe…

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.6 Define $\varphi : \mathbb{R}^\times \rightarrow \{ \pm 1 \}$ by $x \mapsto x / |x|$. Describe…