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## The Boolean ring of subsets is isomorphic to the ring of characteristic functions

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.15 Solution: Let $\Phi : \mathcal{P}(X) \rightarrow {}^X\mathbb{Z}/(2)$ be the mapping given by $A \mapsto \chi_A$, and…

## 2Z and 3Z are not isomorphic as rings

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.1 Prove that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic. Solution: Suppose \$\varphi : 2\mathbb{Z} \rightarrow…