Consider the set ##V = \left \{ f : f \text{is any real-valued function of one real variable}\right \}##. I believe that ##V## is a vector space over the field ##\mathbb{R}##, since for all ##f,g \in V## and ##a,b \in \mathbb{R}##, it is true that ##0 \in V##, ##af-bg \in V##, ##af+ag = a(f+g)##, and ##(ab)f = a(bf)##. (Forgive me if I've missed something or used strange vocabulary or symbology!)(adsbygoogle = window.adsbygoogle || []).push({});

The thing is, ##V## is not only a group under addition, but also a group under multiplication: ##\frac{af}{bg} \in V##. Is there a special name for a vector space that is also a field? Thanks!

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# Does this kind of space have a name?

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