Dummit And Foote Solutions Chapter 14 -

Students often forget to verify that these maps are indeed automorphisms (i.e., they respect addition and multiplication). The solution must mention that because $\sqrt2$ and $\sqrt3$ are linearly independent over $\mathbbQ$, the maps extend uniquely.

To illustrate the nature of the solutions in Chapter 14, we analyze three representative problems typically found in the text. Dummit And Foote Solutions Chapter 14