Dummit And Foote Solutions Chapter 7 //top\\ -

The worst solutions are one-line answers: "$5\mathbbZ$ is an ideal." The best solutions write: "First, note $5\mathbbZ$ is an additive subgroup because... Second, for any $r\in \mathbbZ$, $r\cdot 5k = 5(rk) \in 5\mathbbZ$, and similarly $5k \cdot r \in 5\mathbbZ$. Hence it absorbs multiplication."

Then comes Chapter 7: "Introduction to Rings." The psychological whiplash is real. You leave a world with one binary operation (group multiplication) and enter a world with two operations: addition and multiplication. Suddenly, you must juggle: dummit and foote solutions chapter 7

While working through Chapter 7, it is helpful to cross-reference your proofs with established solution sets. The worst solutions are one-line answers: "$5\mathbbZ$ is

This section connects ring theory to number theory and algebraic geometry. Problems include: for any $r\in \mathbbZ$