## 305 -Fields (4)

February 20, 2009

Suppose that ${\mathbb F}$ is a field and that $S\subset{\mathbb F}.$ It may be that $S$ is also a field, using the same operations of ${\mathbb F}.$ For example, if ${\mathbb F}={\mathbb R},$ then we could have $S={\mathbb Q}.$

Definition 15. If ${\mathbb F}$ is a field and $S\subset{\mathbb F},$ we say that $S$ is a subfield of ${\mathbb F}$ if $S$ is a field with the operations of ${\mathbb F}.$