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## Each field of characteristic zero contains a copy of the rational number field

Solution to Linear Algebra Hoffman & Kunze Chapter 1.2 Exercise 1.2.8 Solution: Call the additive and multiplicative identities of $\mb F$ $0_{\mb F}$ and $1_{\mb F}$ respectively. Define $n_{\mb F}$…

## Each subfield of the field of complex numbers contains every rational number

Solution to Linear Algebra Hoffman & Kunze Chapter 1.2 Exercise 1.2.7 Solution: Every subfield of $\C$ has characterisitc zero since if $\mb F$ is a subfield then $1\in \mb F$…

## Decide whether a given set of rationals is a subring

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.5 Decide which of the following are subrings of $\mathbb{Q}$. (1) The set of all rational numbers…