Notation for the Dual of a Vector Space

[Mandelbroth]

I've been reading about algebraic geometry lately. I see that a lot of authors use $V^\vee$ to denote the dual space of a vector space $V$. Is there any particular reason for this?

The only reason I could think of is that this notation leaves us free to use $R^*$ to denote the units of $R$. However, this still doesn't make sense of the reasoning behind the notation.

Thank you!

 

[Bacle2]

What do you mean by the units of R, how do you define the dual of a ring? Do you define the ring as a module over itself and then define its dual?

 

[Mandelbroth]

What do you mean by the units of R, how do you define the dual of a ring? Do you define the ring as a module over itself and then define its dual?

Sorry. I'm saying that the notation prevents confusion between the dual of a vector space and the group of units of a ring. The question is why the "\vee" is used.